arXiv subjects

Zhenya Yan

Publications and source records attributed to Zhenya Yan.

At least 19 recordsLinked to original sources

arXiv2026

Long-time asymptotics of the integrable defocusing Wadati-Konno-Ichikawa equation with a finite-genus algebro-geometric background

We study the finite-genus algebro-geometric solutions of the Wadati-Konno-Ichikawa (WKI) equation with the saturable nonlinearity and long-time asymptotic behaviors of their short-range perturbations. First, for both the focusing and defocusing reductions, we formulate the finite-genus Baker-Akhiezer functions as explicitly solvable the matrix Riemann-Hilbert (RH) problems on the complex spectral plane and obtain theta-function representations together with the reconstruction formulae for the WKI field and the reciprocal coordinate. We then consider the Cauchy problem of the defocusing WKI equation on a finite-genus algebro-geometric background. We construct the scattering data and RH problem, and perform a Deift-Zhou nonlinear steepest descent analysis. The space-time plane is divided into two transition regions, a Zakharov-Manakov (ZM) region, and a fast-decay region. The leading term is a phase-shifted finite-genus WKI solution. The transition corrections are governed by a Painlev\'e-XXXIV model, while the ZM radiation is described by parabolic-cylinder functions. The reciprocal-coordinate asymptotics are obtained simultaneously.

nlin.SI↗

arXiv2026

On the global well-posedness for the nonlocal Fokas-Lenells equation with the weighted Sobolev initial data on the line

We establish the global well-posedness of the Cauchy problem for the reverse space-time nonlocal Fokas-Lenells equation with the weighted Sobolev initial data $q_0(x)\in H^{3}(\mathbb{R}) \cap H^{2,1}(\mathbb{R})$ on the line. We develop the inverse scattering transform formulated via the associated Riemann-Hilbert problems to study this issue. A spectral uniformization transform is introduced to resolve the singular behavior inherent in the KN-type negative flow spectral problem. Owing to the reverse space-time reduction, reflection coefficients no longer satisfy the usual Hermitian conjugation symmetry, and the coercivity of the jump matrix is therefore not available a priori. The quantitative smallness condition on the initial data yields uniform bounds on the reflection coefficients and ensures the uniform positive definiteness of the Hermitian part of the associated jump matrix. The resulting coercivity allows us to establish the bounded invertibility of the associated singular integral operator through a Fredholm and vanishing-lemma argument. Under this condition, we prove an $L^{2}$-Sobolev bijective correspondence between the potential and scattering data, exclude spectral singularities on continuous spectra, and obtain the global existence and uniqueness of solutions. Moreover, the associated solution map is Lipschitz continuous on the admissible initial-data class.

nlin.SI↗

arXiv2026

Long-time asymptotic behavior for the defocusing Hirota equation on a finite-genus algebro-geometric background

In this paper, we investigate the long-time asymptotics for the solution of the Cauchy problem of the defocusing Hirota equation on a finite-genus algebro-geometric background in the whole $(x,t)$-half-plane, whose method is mainly based on a Riemann-Hilbert (RH) formulation and Deift-Zhou nonlinear steepest descent method. The critical values of the phase function in the associated RH problem divide the space-time plane into four regions, in which the leading-order term is given by a phase-shifted finite-genus algebro-geometric solution. The subleading behavior depends on the region: the correction is of order $t^{-1/3}$ and is governed by a Painlev\'e-XXXIV model RH problem in the transition regions; the leading radiation is of order $t^{-1/2}$ in the Zakharov--Manakov region; and the error is $O(t^{-1})$ in the fast-decay region. These results can also be extended to other higher-order members of the AKNS hierarchy.

nlin.SI↗

arXiv2025

Efficient High-Accuracy PDEs Solver with the Linear Attention Neural Operator

Neural operators offer a powerful data-driven framework for learning mappings between function spaces, in which the transformer-based neural operator architecture faces a fundamental scalability-accuracy trade-off: softmax attention provides excellent fidelity but incurs quadratic complexity $\mathcal{O}(N^2 d)$ in the number of mesh points $N$ and hidden dimension $d$, while linear attention variants reduce cost to $\mathcal{O}(N d^2)$ but often suffer significant accuracy degradation. To address the aforementioned challenge, in this paper, we present a novel type of neural operators, Linear Attention Neural Operator (LANO), which achieves both scalability and high accuracy by reformulating attention through an agent-based mechanism. LANO resolves this dilemma by introducing a compact set of $M$ agent tokens $(M \ll N)$ that mediate global interactions among $N$ tokens. This agent attention mechanism yields an operator layer with linear complexity $\mathcal{O}(MN d)$ while preserving the expressive power of softmax attention. Theoretically, we demonstrate the universal approximation property, thereby demonstrating improved conditioning and stability properties. Empirically, LANO surpasses current state-of-the-art neural PDE solvers, including Transolver with slice-based softmax attention, achieving average $19.5\%$ accuracy improvement across standard benchmarks. By bridging the gap between linear complexity and softmax-level performance, LANO establishes a scalable, high-accuracy foundation for scientific machine learning applications.

cs.LG↗

arXiv2025

Asymmetric integrable turbulence and rogue wave statistics for the derivative nonlinear Schr\"odinger equation

We investigate the asymmetric integrable turbulence and rogue waves (RWs) emerging from the modulation instability (MI) of plane waves for the DNLS equation. The $n$-th moments and ensemble-averaged kinetic and potential energy exhibit oscillatory convergence towards their steady-state values. Specifically, the amplitudes of oscillations for these indexes decay asymptotically with time as $t^{-1.36}$, while the phase shifts demonstrate a nonlinear decay with a rate of $t^{-0.78}$. The frequency of these oscillations is observed to be twice the maximum growth rate of MI. These oscillations can be classified into two distinct types: one is in phase with ensemble-averaged potential energy modulus $|\langle H_4\rangle|$, and the other is anti-phase. At the same time, this unity is also reflected in the wave-action spectrum $ S_k(t) $ for a given $ k $, the auto-correlation function $ g(x,t) $ for a given $ x $, as well as the PDF $ P(I,t) $. The critical feature of the turbulence is the wave-action spectrum, which follows a power-law distribution of $ |k+3|^{-\alpha} $ expect for $k=-3$. Unlike the NLS equation, the turbulence in the DNLS setting is asymmetric, primarily due to the asymmetry between the wave number of the plane wave from the MI and the perturbation wave number.. As the asymptotic peak value of $ S_k $ is observed at $ k = -3 $, the auto-correlation function exhibits a nonzero level as $ x \to \pm L/2 $. The PDF of the wave intensity asymptotically approaches the exponential distribution in an oscillatory manner. However, during the initial stage of the nonlinear phase, MI slightly increases the occurrence of RWs. This happens at the moments when the potential modulus is at its minimum, where the probability of RWs occurring in the range of $ I\in [12, 15] $ is significantly higher than in the asymptotic steady state.

nlin.SI↗

arXiv2025

PMNO: A novel physics guided multi-step neural operator predictor for partial differential equations

Neural operators, which aim to approximate mappings between infinite-dimensional function spaces, have been widely applied in the simulation and prediction of physical systems. However, the limited representational capacity of network architectures, combined with their heavy reliance on large-scale data, often hinder effective training and result in poor extrapolation performance. In this paper, inspired by traditional numerical methods, we propose a novel physics guided multi-step neural operator (PMNO) architecture to address these challenges in long-horizon prediction of complex physical systems. Distinct from general operator learning methods, the PMNO framework replaces the single-step input with multi-step historical data in the forward pass and introduces an implicit time-stepping scheme based on the Backward Differentiation Formula (BDF) during backpropagation. This design not only strengthens the model's extrapolation capacity but also facilitates more efficient and stable training with fewer data samples, especially for long-term predictions. Meanwhile, a causal training strategy is employed to circumvent the need for multi-stage training and to ensure efficient end-to-end optimization. The neural operator architecture possesses resolution-invariant properties, enabling the trained model to perform fast extrapolation on arbitrary spatial resolutions. We demonstrate the superior predictive performance of PMNO predictor across a diverse range of physical systems, including 2D linear system, modeling over irregular domain, complex-valued wave dynamics, and reaction-diffusion processes. Depending on the specific problem setting, various neural operator architectures, including FNO, DeepONet, and their variants, can be seamlessly integrated into the PMNO framework.

cs.LG↗

arXiv2025

Rigorous analysis of large-space and long-time asymptotics for the short-pulse soliton gases

We rigorously analyze the asymptotics of soliton gases to the short-pulse (SP) equation. The soliton gas is formulated in terms of a RH problem, which is derived from the RH problems of the $N$-soliton solutions with $N \to \infty$. Building on prior work in the study of the KdV soliton gas and orthogonal polynomials with Jacobi-type weights, we extend the reflection coefficient to two generalized forms on the interval $\left[\eta_1, \eta_2\right]$: $r_0(\lambda) = \left(\lambda - \eta_1\right)^{\beta_1}\left(\eta_2 - \lambda\right)^{\beta_2}|\lambda - \eta_0|^{\beta_0}\gamma(\lambda)$, $r_c(\lambda) = \left(\lambda - \eta_1\right)^{\beta_1}\left(\eta_2 - \lambda\right)^{\beta_2}\chi_c(\lambda)\gamma(\lambda)$, where $0 < \eta_1 < \eta_0 < \eta_2$ and $\beta_j > -1$ ($j = 0, 1, 2$), $\gamma(\lambda)$ is continuous and positive on $\left[\eta_1, \eta_2\right]$, with an analytic extension to a neighborhood of this interval, $\chi_c(\lambda) = 1$ for $\lambda \in \left[\eta_1, \eta_0\right)$ and $\chi_c(\lambda) = c^2$ for $\lambda \in \left(\eta_0, \eta_2\right]$, where $c>0$ with $c \neq 1$. The asymptotic analysis is performed using the steepest descent method. A key aspect of the analysis is the construction of the $g$-function. To address the singularity at the origin, we introduce an innovative piecewise definition of $g$-function. To establish the order of the error term, we construct local parametrices near $\eta_j$ for $j = 1, 2$, and singularity $\eta_0$. At the endpoints, we employ the Airy parametrix and the first type of modified Bessel parametrix. At the singularity $\eta_0$, we use the second type of modified Bessel parametrix for $r_0$ and confluent hypergeometric parametrix for $r_c(\lambda)$.

nlin.SI↗

arXiv2025

Long-time asymptotics for the $N_{\infty}$-soliton solution to the KdV equation with two types of generalized reflection coefficients

We systematically investigate the long-time asymptotics for the $N_{\infty}$-soliton solution to the KdV equation in the different regions with the aid of the Riemann-Hilbert (RH) problems with two types of generalized reflection coefficients on the interval $\left[\eta_1, \eta_2\right]\in \mathbb{R}^+$: $r_0(\lambda,\eta_0; \beta_0, \beta_1,\beta_2)=\left(\lambda-\eta_1\right)^{\beta_1}\left(\eta_2-\lambda\right)^{\beta_2}\left|\lambda-\eta_0\right|^{\beta_0}\gamma\left(\lambda\right)$, $r_c(\lambda,\eta_0; \beta_1,\beta_2)=\left(\lambda-\eta_1\right)^{\beta_1}\left(\eta_2-\lambda\right)^{\beta_2}\chi_c\left(\lambda, \eta_0\right)\gamma \left(\lambda\right)$, where the singularity $\eta_0\in (\eta_1, \eta_2)$ and $\beta_j>-1$ ($j=0, 1, 2$), $\gamma: \left[\eta_1, \eta_2\right] \to\mathbb{R}^+$ is continuous and positive on $\left[\eta_1, \eta_2\right]$, with an analytic extension to a neighborhood of this interval, and the step-like function $\chi_c$ is defined as $\chi_c\left(\lambda,\eta_0\right)=1$ for $\lambda\in\left[\eta_1, \eta_0\right)$ and $\chi_c\left(\lambda,\eta_0\right)=c^2$ for $\lambda\in\left(\eta_0, \eta_2\right]$ with $c>0, \, c\ne1$. A critical step in the analysis of RH problems via the Deift-Zhou steepest descent technique is how to construct local parametrices around the endpoints $\eta_j$'s and the singularity $\eta_0$. Specifically, the modified Bessel functions of indexes $\beta_j$'s are utilized for the endpoints $\eta_j$'s, and the modified Bessel functions of index $\left(\beta_0\pm 1\right)\left/\right.2$ and confluent hypergeometric functions are employed around the singularity $\eta_0$ if the reflection coefficients are $r_0$ and $r_c$, respectively. This comprehensive study extends the understanding of generalized reflection coefficients and provides valuable insights into the asymptotics of soliton gases.

nlin.SI↗

arXiv2025

Breather gas and shielding for the focusing nonlinear Schr\"odinger equation with nonzero backgrounds

Breathers have been experimentally and theoretically found in many physical systems -- in particular, in integrable nonlinear-wave models. A relevant problem is to study the \textit{breather gas}, which is the limit, for $N\rightarrow \infty $, of $N$-breather solutions. In this paper, we investigate the breather gas in the framework of the focusing nonlinear Schr\"{o}dinger (NLS) equation with nonzero boundary conditions, using the inverse scattering transform and Riemann-Hilbert problem. We address aggregate states in the form of $N$-breather solutions, when the respective discrete spectra are concentrated in specific domains. We show that the breather gas coagulates into a single-breather solution whose spectral eigenvalue is located at the center of the circle domain, and a multi-breather solution for the higher-degree quadrature concentration domain. These coagulation phenomena in the breather gas are called \textit{breather shielding}. In particular, when the nonzero boundary conditions vanish, the breather gas reduces to an $n$-soliton solution. When the discrete eigenvalues are concentrated on a line, we derive the corresponding Riemann-Hilbert problem. When the discrete spectrum is uniformly distributed within an ellipse, it is equivalent to the case of the line domain. These results may be useful to design experiments with breathers in physical settings.

nlin.SI↗

arXiv2025

On the $N_\infty$-soliton asymptotics for the modified Camassa-Holm equation with linear dispersion and vanishing boundaries

We explore the $N_{\infty}$-soliton asymptotics for the modified Camassa-Holm (mCH) equation with linear dispersion and boundaries vanishing at infinity: $m_t+(m(u^2-u_x^2)^2)_x+\kappa u_x=0,\quad m=u-u_{xx}$ with $\lim_{x\rightarrow \pm \infty }u(x,t)=0$. We mainly analyze the aggregation state of $N$-soliton solutions of the mCH equation expressed by the solution of the modified Riemann-Hilbert problem in the new $(y,t)$-space when the discrete spectra are located in different regions. Starting from the modified RH problem, we find that i) when the region is a quadrature domain with $\ell=n=1$, the corresponding $N_{\infty}$-soliton is the one-soliton solution which the discrete spectral point is the center of the region; ii) when the region is a quadrature domain with $\ell=n$, the corresponding $N_{\infty}$-soliton is an $n$-soliton solution; iii) when the discrete spectra lie in the line region, we provide its corresponding Riemann-Hilbert problem,; and iv) when the discrete spectra lie in an elliptic region, it is equivalent to the case of the line region.

nlin.SI↗

arXiv2025

On Large-Space and Long-Time Asymptotic Behaviors of Kink-Soliton Gases in the Sine-Gordon Equation

We conduct a comprehensive analysis of the large-space and long-time asymptotics of kink-soliton gases in the sine-Gordon (sG) equation, addressing an important open problem highlighted in the recent work [Phys. Rev. E 109 (2024) 061001]. We focus on kink-soliton gases modeled within a Riemann-Hilbert framework and characterized by two types of generalized reflection coefficients, each defined on the interval $[\eta_1, \eta_2]$: $r_0(\lambda) = (\lambda - \eta_1)^{\beta_1} (\eta_2 - \lambda)^{\beta_2} |\lambda - \eta_0|^{\beta_0} \gamma(\lambda)$ and $r_c(\lambda) = (\lambda - \eta_1)^{\beta_1} (\eta_2 - \lambda)^{\beta_2} \chi_c(\lambda) \gamma(\lambda)$, where $0 < \eta_1 < \eta_0 < \eta_2$ and $\beta_j > -1$, $\gamma(\lambda)$ is a continuous, strictly positive function defined on $[\eta_1, \eta_2]$. The function $\chi_c(\lambda)$ demonstrates a step-like behavior: it is given by $\chi_c(\lambda) = 1$ for $\lambda \in [\eta_1, \eta_0)$ and $\chi_c(\lambda) = c^2$ for $\lambda \in (\eta_0, \eta_2]$, with $c$ as a positive constant distinct from one. To rigorously derive the asymptotic results, we leverage the Deift-Zhou steepest descent method. A central component of this approach is constructing an appropriate $g$-function for the conjugation process. Unlike in the KdV equation, the sG presents unique challenges for $g$-function formulation, particularly concerning the singularity at the origin. The Riemann-Hilbert problem also requires carefully constructed local parametrices near endpoints $\eta_j$ and the singularity $\eta_0$. At the endpoints $\eta_j$, we employ a modified Bessel parametrix of the first kind. For the singularity $\eta_0$, the parametrix selection depends on the reflection coefficient: the second kind of modified Bessel parametrix is used for $r_0(\lambda)$, while a confluent hypergeometric parametrix is applied for $r_c(\lambda)$.

nlin.SI↗

arXiv2024

The focusing complex mKdV equation with nonzero background: Large $N$-order asymptotics of multi-rational solitons and related Painlev\'{e}-III hierarchy

In this paper, we investigate the large-order asymptotics of multi-rational solitons of the focusing complex modified Korteweg-de Vries (c-mKdV) equation with nonzero background via the Riemann-Hilbert problems. First, based on the Lax pair, inverse scattering transform, and a series of deformations, we construct a multi-rational soliton of the c-mKdV equation via a solvable Riemann-Hilbert problem (RHP). Then, through a scale transformation, we construct a RHP corresponding to the limit function which is a new solution of the c-mKdV equation in the rescaled variables $X,\,T$, and prove the existence and uniqueness of the RHP's solution. Moreover, we also find that the limit function satisfies the ordinary differential equations (ODEs) with respect to space $X$ and time $T$, respectively. The ODEs with respect to space $X$ are identified with certain members of the Painlev\'{e}-III hierarchy. We study the large $X$ and transitional asymptotic behaviors of near-field limit solutions, and we provide some part results for the case of large $T$. These results will be useful to understand and apply the large-order rational solitons in the nonlinear wave equations.

nlin.SI↗

arXiv2024

Is the neural tangent kernel of PINNs deep learning general partial differential equations always convergent ?

In this paper, we study the neural tangent kernel (NTK) for general partial differential equations (PDEs) based on physics-informed neural networks (PINNs). As we all know, the training of an artificial neural network can be converted to the evolution of NTK. We analyze the initialization of NTK and the convergence conditions of NTK during training for general PDEs. The theoretical results show that the homogeneity of differential operators plays a crucial role for the convergence of NTK. Moreover, based on the PINNs, we validate the convergence conditions of NTK using the initial value problems of the sine-Gordon equation and the initial-boundary value problem of the KdV equation.

stat.ML↗

arXiv2024

Two-dimensional fractional discrete NLS equations: dispersion relations, rogue waves, fundamental and vortex solitons

We introduce physically relevant new models of two-dimensional (2D) fractional lattice media accounting for the interplay of fractional intersite coupling and onsite self-focusing. Our approach features novel discrete fractional operators based on an appropriately modified definition of the continuous Riesz fractional derivative. The model of the 2D isotropic lattice employs the discrete fractional Laplacian, whereas the 2D anisotropic system incorporates discrete fractional derivatives acting independently along orthogonal directions with different L\'evy indices (LIs). We derive exact linear dispersion relations (DRs), and identify spectral bands that permit linear modes to exist, finding them to be similar to their continuous counterparts, apart from differences in the wavenumber range. Additionally, the modulational instability in the discrete models is studied in detail, and, akin to the linear DRs, it is found to align with the situation in continuous models. This consistency highlights the nature of our newly defined discrete fractional derivatives. Furthermore, using Gaussian inputs, we produce a variety of rogue-wave structures. By means of numerical methods, we systematically construct families of 2D fundamental and vortex solitons, and examine their stability. Fundamental solitons maintain the stability due to the discrete nature of the interactions, preventing the onset of the critical and supercritical collapse. On the other hand, vortex solitons are unstable in the isotropic lattice model. However, the anisotropic one -- in particular, its symmetric version with equal LIs acting in both directions -- maintains stable vortex solitons with winding numbers $S=1$ and $S=3$. The detailed results stress the robustness of the newly defined discrete fractional Laplacian in supporting well-defined soliton modes in the 2D lattice media.

nlin.PS↗

arXiv2024

Data-driven 2D stationary quantum droplets and wave propagations in the amended GP equation with two potentials via deep neural networks learning

In this paper, we develop a systematic deep learning approach to solve two-dimensional (2D) stationary quantum droplets (QDs) and investigate their wave propagation in the 2D amended Gross-Pitaevskii equation with Lee-Huang-Yang correction and two kinds of potentials. Firstly, we use the initial-value iterative neural network (IINN) algorithm for 2D stationary quantum droplets of stationary equations. Then the learned stationary QDs are used as the initial value conditions for physics-informed neural networks (PINNs) to explore their evolutions in the some space-time region. Especially, we consider two types of potentials, one is the 2D quadruple-well Gaussian potential and the other is the PT-symmetric HO-Gaussian potential, which lead to spontaneous symmetry breaking and the generation of multi-component QDs. The used deep learning method can also be applied to study wave propagations of other nonlinear physical models.

cs.LG↗

arXiv2024

Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations

We propose a new two-stage initial-value iterative neural network (IINN) algorithm for solitary wave computations of nonlinear wave equations based on traditional numerical iterative methods and physics-informed neural networks (PINNs). Specifically, the IINN framework consists of two subnetworks, one of which is used to fit a given initial value, and the other incorporates physical information and continues training on the basis of the first subnetwork. Importantly, the IINN method does not require any additional data information including boundary conditions, apart from the given initial value. Corresponding theoretical guarantees are provided to demonstrate the effectiveness of our IINN method. The proposed IINN method is efficiently applied to learn some types of solutions in different nonlinear wave equations, including the one-dimensional (1D) nonlinear Schr\"odinger equations (NLS) equation (with and without potentials), the 1D saturable NLS equation with PT -symmetric optical lattices, the 1D focusing-defocusing coupled NLS equations, the KdV equation, the two-dimensional (2D) NLS equation with potentials, the 2D amended GP equation with a potential, the (2+1)-dimensional KP equation, and the 3D NLS equation with a potential. These applications serve as evidence for the efficacy of our method. Finally, by comparing with the traditional methods, we demonstrate the advantages of the proposed IINN method.

physics.comp-ph↗

arXiv2024

Suppression of soliton collapses, modulational instability, and rogue-wave excitation in two-L\'evy-index fractional Kerr media

s in laser systems with two fractional-dispersion/diffraction terms, quantified by their L\'{e}vy indices, $\alpha_{1}\, \alpha_{2}\in (1, 2]$, and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic fractional nonlinear Schr\"{o}dinger equation with only one L\'{e}vy index $\alpha =1$, can be suppressed in the two-L\'{e}vy-index fractional nonlinear Schr\"{o}dinger system. Stability of the solitons is also explored against collisions with Gaussian pulses and adiabatic variation of the system parameters. Modulation instability of continuous waves is investigated in the two-L\'{e}vy-index system too. In particular, the modulation instability may occur in the case of the defocusing nonlinearity when two diffraction coefficients have opposite signs. Using results for the modulation instability, we produce first- and second-order rogue waves on top of continuous waves, for both signs of the Kerr nonlinearity.

nlin.PS↗

arXiv2024

Dynamics of discrete solitons in the fractional discrete nonlinear Schr\"odinger equation with the quasi-Riesz derivative

We elaborate a fractional discrete nonlinear Schr\"{o}dinger (FDNLS) equation based on an appropriately modified definition of the Riesz fractional derivative, which is characterized by its L\'{e}vy index (LI). This FDNLS equation represents a novel discrete system, in which the nearest-neighbor coupling is combined with long-range interactions, that decay as the inverse square of the separation between lattice sites. The system may be realized as an array of parallel quasi-one-dimensional Bose-Einstein condensates composed of atoms or small molecules carrying, respectively, a permanent magnetic or electric dipole moment. The dispersion relation (DR) for lattice waves and the corresponding propagation band in the system's linear spectrum are found in an exact form for all values of LI. The DR is consistent with the continuum limit, differing in the range of wavenumbers. Formation of single-site and two-site discrete solitons is explored, starting from the anti-continuum limit and continuing the analysis in the numerical form up to the existence boundary of the discrete solitons. Stability of the solitons is identified in terms of eigenvalues for small perturbations, and verified in direct simulations. Mobility of the discrete solitons is considered too, by means of an estimate of the system's Peierls-Nabarro potential barrier, and with the help of direct simulations. Collisions between persistently moving discrete solitons are also studied.

nlin.PS↗