arXiv subjects

Yan-Hong Qin

Publications and source records attributed to Yan-Hong Qin.

12 recordsLinked to original sources

arXiv2026

Multihump-Multivalley Soliton Families on a Plane Wave Background in Birefringent Optical Fibers

We obtain a family of multihump-multivalley solitons (MHMVSs) on a plane-wave background in birefringent optical fibers governed by the two-component Fokas-Lenells equations, with exact solutions derived via the Darboux transformation method. The fundamental solutions are systematically classified through their phase diagrams, and higher-order configurations are identified as well. Notably, the construction extends to solitons with arbitrary MHMV structures, a class of solutions previously unreported in two-component integrable systems. Numerical simulations confirm the robustness of these solutions under weak white noise. Furthermore, analysis of their topological structure reveals that the virtual monopole field is determined equally by the intensity zeros and poles of MHMVSs in the complex plane, a feature that has remained unrecognized in previous studies of nonlinear wave topological phases. These findings reveal a previously unknown soliton family on a plane-wave background along with a distinct topological feature within the two-component framework, thereby enriching the broader understanding of topological phases of nonlinear waves.

nlin.PS↗

arXiv2026

Controllable excitation of vector Akhmediev breather patterns

In the focusing Manakov system, multiple modulation instability (MI) branches coexist on the same plane wave background, so the usual weak periodic modulation cannot selectively excite a single vector Akhmediev breather (AB). Here we propose an eigenvector-based initial perturbation scheme that constructs the initial condition as a plane wave plus Fourier modes whose coefficients follow the perturbation eigenvector of a selected MI branch, enabling controllable high-fidelity excitation of desired vector ABs. Numerical simulations show near-100\% fidelity with the exact AB solution. The underlying mechanism is eigenvector-controlled mode selection. The initial seeding of the target MI branch through the chosen eigenvector, together with the non-Hermitian coupling inherent in the linearized MI dynamics, ensures that the targeted unstable mode dominates the early linear stage and thereby dictates the breather type. This eigenvector-based control succeeds in gain-balanced regimes and when the targeted branch has a sufficient gain advantage. The proposed method provides a simple and robust framework for controllable generation of vector ABs over a broad parameter range, highlighting the key role of eigenvector selectivity in multi-component nonlinear systems.

nlin.PS↗

arXiv2026

Dirac monopole potentials with high charges underlying nonlinear waves

We investigate topological vector potentials underlying the phases of nonlinear waves by performing Dirac's magnetic monopole theory in an extended complex plane, taking into account self-steepening effects while ignoring the usual cubic nonlinearities. We uncover that the simple poles and third-order poles of the density function constitute virtual monopole fields with higher charges $\pm3/2$ and $\pm5/2$, respectively. These results are in sharp contrast to the previous findings, where the simple zeros of the density function yield charges $\pm1/2$. We choose scalar and vector rogue waves as well as bright solitons to demonstrate the Dirac monopole potentials. These results confirm a series of quantized magnetic charges for virtual monopoles underlying nonlinear waves, and reveal new relations between poles of density functions and topological charges.

nlin.PS↗

arXiv2025

Varied Branches of Nondegenerate Vector Solitons

Our study on nondegenerate dark-bright-bright solitons in a three-component Manakov model with repulsive interactions reveals the existence of diverse branches of nondegenerate vector solitons. For fixed bright component particle numbers and a given soliton velocity, the nondegenerate dark-bright-bright solitons exhibit four distinct branches with different density profiles and phase distributions, comprising two positive mass branches and two negative mass branches. The energy-velocity dispersion relation of each pair of positive- and one negative-mass branches form a closed loop, resulting in two mutually independent loops for the soliton's overall dispersion. All soliton branches share a common maximal velocity, which is determined by the larger bright soliton particle number. Linear stability analysis shows that all these branches are stable against weak perturbations. Extending to an $N$-component Manakov system, the nondegenerate solitons have $2^{N-1}$ distinct branches, of which $2^{N-2}$ branches solitons is positive mass and $2^{N-2}$ branches solitons is negative mass. Each pair of positive- and negative-mass branches form a closed dispersion relation loop, so that the vector solitons have $2^{N-2}$ disjoint loops. These results uncover the rich branches and interesting dispersion relations of nondegenerate vector solitons in multi-component models.

nlin.PS↗

arXiv2025

A corresponding relationship between nonlinear Hermitian systems and linear non-Hermitian models

We note that the non-orthogonality of states and their coincidence at the degeneracy point are both admitted by nonlinear Hermitian systems and linear non-Hermitian systems. These striking characteristics motivate us to re-investigate the localized waves of nonlinear Hermitian systems and the eigenvalue degeneracies of linear non-Hermitian models, based on several well-known Lax integrable systems that have wide applications in nonlinear optics. We choose nonlinear Schrodinger equation integrability hierarchy to demonstrate the quantitative relations between dynamics of nonlinear Hermitian systems and eigenvalue degeneracies of linear non-Hermitian models. Specifically, the degeneracies of the real or imaginary spectrum of the linear non-Hermitian matrices are uncovered to clarify several essential characteristics of nonlinear localized waves, such as breathers, rogue waves, and solitons. We find that the exceptional points generally correspond to rogue waves for modulational instability cases and dark solitons with maximum velocity for the modulational stability cases. These insights provide another interesting perspective for understanding nonlinear localized waves, and hint that there are closer relations between nonlinear Hermitian systems and linear non-Hermitian systems.

nlin.PS↗

arXiv2022

The optical rogue wave patterns in coupled defocusing systems

We systematically investigate rogue wave's spatial-temporal pattern in $N$ $(N\geq2)$-component coupled defocusing nonlinear Schrödinger equations. The fundamental rogue wave solutions are given in a unified form for both focusing and defocusing cases. We establish the quantitative correspondence between modulation instability and rogue wave patterns, which develops the previously reported inequality relation into an equation correspondence. As an example, we demonstrate phase diagrams for rogue wave patterns in a two-component coupled system, based on the complete classification of their spatial-temporal structures. The phase diagrams enable us to predict various rogue wave patterns, such as the ones with a four-petaled structure in both components. These results are meaningful for controlling the rogue wave excitations in two orthogonal polarization optical fibers.

nlin.PS↗

arXiv2022

Phase Characters of Optical Dark Solitons with the Third-order Dispersion and Delayed Nonlinear Response

Dark soliton is usually seen as one of the simplest topological solitons, due to the phase jump across its density dip. We investigate the phase jump properties of dark solitons in a single mode optical fiber with the third-order dispersion and delayed nonlinear response, based on exact analytical solutions of Hirota equation. Our analysis indicates that a single-valley dark soliton (SVDS) can admit two distinct phase jumps at the same velocity, in sharp contrast to the dark soliton with only the second-order dispersion and self-phase modulation, which admits a one-to-one match between the velocity and phase jump. We further uncover the different topological vector potentials underlying the distinct phase jumps. The relations between phase jump and velocity of the SVDS can explain the generation of the previously reported double-valley dark soliton (DVDS). The detailed analysis on the two phase jumps characters of the DVDS with one identical velocity enables us to obtain U-shaped type or double-step type phase distribution. We further explore collision properties of the DVDSs by analyzing their topological phase, which can be considered as the generalization of topological phase (Phys. Rev. E 103, L040204). Strikingly, the inelastic collision can lead to the conversion between the two types of phase distributions for DVDS. The results reveal that inelastic or elastic collision can be judged by analyzing the magnetic monopole fields.

nlin.PS↗

arXiv2021

Multivalley dark solitons in multicomponent Bose-Einstein condensates with repulsive interactions

We obtain multivalley dark soliton solutions with asymmetric or symmetric profiles in multicomponent repulsive Bose-Einstein condensates by developing the Darboux transformation method. We demonstrate that the width-dependent parameters of solitons significantly affect the velocity ranges and phase jump regions of multivalley dark solitons, in sharp contrast to scalar dark solitons. For double-valley dark solitons, we find that the phase jump is in the range $[0,2π]$, which is quite different from that of the usual single-valley dark soliton. Based on our results, we argue that the phase jump of an $n$-valley dark soliton could be in the range $[0,nπ]$, supported by our analysis extending up to five-component condensates. The interaction between a double-valley dark soliton and a single-valley dark soliton is further investigated, and we reveal a striking collision process in which the double-valley dark soliton is transformed into a breather after colliding with the single-valley dark soliton. Our analyses suggest that this breather transition exists widely in the collision processes involving multivalley dark solitons. The possibilities for observing these multivalley dark solitons in related Bose-Einstein condensates experiments are discussed.

nlin.PS↗

arXiv2020

Classification of Dark Solitons via Topological Vector Potentials

Dark soliton is one of most interesting nonlinear excitations in physical systems, manifesting a spatially localized density "dip" on a uniform background accompanied with a phase jump across the dip. However, the topological properties of the dark solitons are far from fully understood. Our investigation for the first time uncover a vector potential underlying the nonlinear excitation whose line integral gives the striking phase jump. More importantly, we find that the vector potential field has a topological configuration in analogous to the Wess-Zumino term in a Lagrangian representation. It can induce some point-like magnetic fields scattered periodically on a complex plane, each of them has a quantized magnetic flux of elementary $π$. We then calculate the Euler characteristic of the topological manifold of the vector potential field and classify all known dark solitions according to the index.

nlin.PS↗

arXiv2019

A direct derivation of the dark soliton excitation energy

Dark solitons are common topological excitations in a wide array of nonlinear waves. The dark soliton excitation energy, crucial for exploring dark soliton dynamics, is necessarily calculated in a renormalized form due to its existence on a finite background. Despite its tremendous importance and success, the renormalized energy form was firstly only suggested with no detailed derivation, and was then "derived" in the grand canonical ensemble. In this work, we revisit this fundamental problem and provide an alternative and intuitive derivation of the energy form from the fundamental field energy by utilizing a limiting procedure that conserves number of particles. Our derivation yields the same result, putting therefore the dark soliton energy form on a solid basis.

nlin.PS↗

arXiv2019

Spin Solitons in Spin-1 Bose-Einstein Condensates

Solitons in multi-component Bose-Einstein condensates have been paid much attention, due to the stability and wide applications of them. The exact soliton solutions are usually obtained for integrable models. In this paper, we present four families of exact spin soliton solutions for non-integrable cases in spin-1 Bose-Einstein Condensates. The whole particle density is uniform for the spin solitons, which is in sharp contrast to the previously reported solitons of integrable models. The spectrum stability analysis and numerical simulation indicate the spin solitons can exist stably. The spin density redistribution happens during the collision process, which depends on the relative phase and relative velocity between spin solitons. The non-integrable properties of the systems can bring spin solitons experience weak amplitude and location oscillations after collision. These stable spin soliton excitations could be used to study the negative inertial mass of solitons, the dynamics of soliton-impurity systems, and the spin dynamics in Bose-Einstein condensates.

cond-mat.quant-gas↗

arXiv2019

Interference properties of two-component matter wave solitons

The wave properties of solitons in a two-component Bose-Einstein condensates with attractive interactions or repulsive interactions are investigated in detail. We demonstrate that dark solitons in one of component admit interference and tunneling behaviour, in sharp contrast to the scalar dark solitons and vector dark solitons. The analytic analysis of interference properties shows that spatial interference pattern is determined by the relative velocity of solitons, while temporal interference pattern depends on the velocities and widths of two solitons, differing from the interference properties of scalar bright solitons. Especially, for attractive interactions system, we show that interference effects can induce some short-time density humps (whose densities are higher than background density) during the collision process of dark solitons. Moreover, the maximum hump value is remarkably sensitive to the variation of the solitons' parameters. For repulsive interactions system, the temporal-spatial interference periods have lower limits. Numerical simulations results suggest that interference patterns for dark-bright solitons are more robust against noises than bright-dark solitons. These explicit interference properties can be used to measure the velocities and widths of solitons. It is expected that these interference behaviour can be observed experimentally and could be used to design matter wave soliton interferometry in vector systems.

nlin.PS↗