arXiv subjects

Wen-Rong Sun

Publications and source records attributed to Wen-Rong Sun.

11 recordsLinked to original sources

arXiv2026

Exact vector Akhmediev breathers dominated by a linearly stable frequency

In the scalar nonlinear Schrodinger equation, an Akhmediev breather (AB) is dominated by a frequency that lies inside the modulation instability gain band. This exactly correspondence between instability and breathers is challenged in vector systems such as the Manakov system, where the gain spectrum splits into disconnected lobes separated by stable gaps. We analytically and numerically construct an AB that is generated by unstable modes but is spectrally dominated by a stable harmonic at its peak. Numerical simulations starting from a simple continuous wave background perturbed only by the unstable harmonics confirm that the stable component emerges spontaneously and becomes dominant without any initial seed. We identify the precise parameter window in which this phenomenon occurs and show that this passive amplification of the linearly stable component is driven by four-wave mixing, which accounts for 96% of the nonlinear forcing. Given the universality of the Manakov system across nonlinear physics, from nonlinear optics to ultracold quantum gases, these results open an experimentally accessible new perspective on breather dynamics, one in which linearly stable frequencies can dominate.

nlin.PS↗

arXiv2025

Nonreciprocity-Enabled Chiral Stability of Nonlinear Waves

The control of wave propagation, particularly the quest for unidirectional transport, plays an important role in photonics and metamaterial science. While nonreciprocity is known to enable unidirectional amplification and stabilize complex solitons, its fundamental impact on the intrinsic stability of the nonlinear waves remains an open frontier. By obtaining exact analytical solutions for a dissipative, nonreciprocal sine-Gordon model (that was proposed in [\emph{Nature} 627, 528-533, 2024] and captures all essential physics of active materials) and performing a comprehensive stability analysis, we discover a chiral stability criterion: waves propagating in one direction exhibit robust stability, while their mirror-image counterparts are intrinsically unstable. This direction-dependent stability is confirmed by full nonlinear simulations. Our findings identify the symmetry-breaking role of nonreciprocity in defining the stability of nonlinear waves, a key step toward controlling wave propagation in nonreciprocal media.

nlin.PS↗

arXiv2025

Dissipative structures in one- and two-dimensional Kerr cavities with a spatially periodic pump

The interplay of periodic driving and dissipation is a fundamental feature of nonequilibrium physics. We elaborate a scenario for the formation of dissipative multi-spot excitations (MSEs) in Kerr cavities, modeled by the one- and two-dimensional (1D and 2D) Lugiato-Lefever (LL) equations, which include a spatially periodic pump (SPP). First, we demonstrate that the SPP produces three novel exact periodic solutions of the LL equation, expressed in terms of the $\mathrm{sn}$, $\mathrm{cn}$, and $\mathrm{dn}$ elliptic functions. By means of numerical methods, we explore the modulational instability (MI) and transverse instability (TI) of the periodic states in 1D and 2D settings, respectively. In the case of the defocusing nonlinearity, the 1D MI breaks the periodic states into an array of spatiotemporal crescents. In the case of self-focusing, the 1D MI, initiated by small random perturbations, leads to establishment of a chaotic state, with the amplitude statistics featuring a long-tail probability distribution, that represents the presence of dissipative rogue waves. On the other hand, spatially periodic perturbations initiate formation of breather chains, which periodically disappear and reappear, resembling the Fermi-Pasta-Ulam-Tsingou recurrence. In the 2D regime, the TI results in the formation of an array of 2D lumps. For a given SPP strength, the exact solutions for the periodic structures are stable if the loss constant exceeds a critical value. The findings reported here provide a contribution to nonequilibrium physics in general and may find direct applications in laser physics.

physics.optics↗

arXiv2024

Rogue waves and instability arising from long-wave-short-wave resonance beyond the integrable regime

We consider instability and localized patterns arising from long wave-short wave (LWSW) resonance in the non-integrable regime numerically. We study the stability and instability of elliptic-function periodic waves with respect to subharmonic perturbations, whose period is a multiple of the period of the elliptic waves. We thus find the modulational instability (MI) of the corresponding dnoidal waves. Upon varying parameters of dnoidal waves, spectrally unstable ones can be transformed into stable states via the Hamiltonian Hopf bifurcation. For snoidal waves, we find a transition of the dominant instability scenario between the MI and instability with a bubble-like spectrum. For cnoidal waves, we produce three variants of the MI. Evolution of the unstable states is also considered, leading to formation of rogue waves on top of the elliptic-wave and continuous-wave backgrounds.

nlin.PS↗

arXiv2023

The instabilities beyond modulational type in a repulsive Bose-Einstein condensate with a periodic potential

The instabilities of the nontrivial phase elliptic solutions in a repulsive Bose-Einstein condensate (BEC) with a periodic potential are investigated. Based on the defocusing nonlinear Schr\"{o}dinger (NLS) equation with an elliptic function potential, the well-known modulational instability (MI), the more recently identified high-frequency instability, and an unprecedented -- to our knowledge -- variant of the MI, the so-called isola instability are identified numerically. Upon varying parameters of the solutions, instability transitions occur through the suitable bifurcations, such as the Hamiltonian Hope one. Specifically, (i) increasing the elliptic modulus $k$ of the solutions, we find that MI switches to the isola instability and the dominant disturbance has twice the elliptic wave's period, corresponding to a Floquet exponent $\mu=\frac{\pi}{2K(k)}$. The isola instability arises from the collision of spectral elements at the origin of the spectral plane. (ii) Upon varying $V_{0}$, the transition between MI and the high-frequency instability occurs. Differently from the MI and isola instability where the collisions of eigenvalues happen at the origin, high-frequency instability arises from pairwise collisions of nonzero, imaginary elements of the stability spectrum; (iii) In the limit of sinusoidal potential, we show that MI occurs from a collision of eigenvalues with $\mu=\frac{\pi}{2K(k)}$ at the origin; (iv) we also examine the dynamic byproducts of the instability in chaotic fields generated by its manifestation. An interesting observation is that, in addition to MI, the isola instability could also lead to dark localized events in the scalar defocusing NLS equation.

nlin.PS↗

arXiv2023

Time-localized dark modes generated by zero-wavenumber-gain modulational instability

In this work we report on the emergence of a novel type of solitary waves, viz., time-localized solitons in integrable and non-integrable variants of the massive Thirring models and in the three-wave resonant-interaction system, which are models broadly used in plasmas, nonlinear optics and hydrodynamics. An essential finding is that the condition for the existence of time-localized dark solitons, which develop density dips in the course of time evolution, in these models coincides with the condition for the occurrence of the zero-wavenumber-gain (ZWG) modulational instability (MI). Systematic simulations reveal that, whenever the ZWG MI is present, patterns reminiscent of such solitons are generically excited from a chaotic background field as fragments within more complex patterns.

nlin.PS↗

arXiv2023

Periodic traveling waves in the \phi^4 model: Instability, stability and localized structures

We consider the instability and stability of periodic stationary solutions to the classical \phi^4 equation numerically. In the superluminal regime, the model possesses dnoidal and cnoidal waves. The former are modulationally unstable and the spectrum forms a figure eight intersecting at the origin of the spectral plane. The latter can be modulationally stable and the spectrum near the origin in that case is represented by vertical bands along the purely imaginary axis. The instability of the cnoidal states in that case stems from elliptical bands of complex eigenvalues far from the spectral plane origin. In the subluminal regime, there exist only snoidal waves which are modulationally unstable. Considering the subharmonic perturbations, we show that the snoidal waves in the subluminal regime are spectrally unstable with respect to all subharmonic perturbations, while for the dnoidal and cnoidal waves in the superluminal regime, the transition between the spectrally stable state and the spectrally unstable state occurs through a Hamiltonian Hopf bifurcation. The dynamical evolution of the unstable states is also considered, leading to some interesting spatio-temporal localization events.

nlin.PS↗

arXiv2022

Formation of rogue waves and modulational instability with zero-wavenumber gain in multi-component systems with coherent coupling

It is known that rogue waves (RWs) are generated by the modulational instability (MI) of the baseband type. Starting with the Bers-Kaup-Reiman system for three-wave resonant interactions, we identify a specific RW-building mechanism based on MI which includes zero wavenumber in the gain band. An essential finding is that this mechanism works solely under a linear relation between the MI gain and a vanishingly small wavenumber of the modulational perturbation. The same mechanism leads to the creation of RWs by MI in other multi-component systems-in particular, in the massive Thirring model.

nlin.PS↗

arXiv2021

The orbital stability of the periodic traveling wave solutions to the defocusing complex modified Korteweg-de Vries equation

The stability of the elliptic solutions to the defocusing complex modified Korteweg-de Vries (cmKdV) equation is studied. The orbital stability of the cmKdV equation was established in [19] when the periodic orbits do not oscillate around zero. In this paper, we study the periodic solutions corresponding to the case that the orbits oscillate around zero. Using the integrability of the defocusing cmKdV equation, we prove the spectral stability of the elliptic solutions. We show that one special linear combination of the first five conserved quantities produces a Lyapunov functional, which implies that the elliptic solutions are orbitally stable with respect to the subharmonic perturbations.

nlin.SI↗

arXiv2020

Stability of elliptic solutions to the sinh-Gordon equation

Using the integrability of the sinh-Gordon equation, we demonstrate the spectral stability of its elliptic solutions. By constructing a Lyapunov functional using higher-order conserved quantities of the sinh-Gordon equation, we show that these elliptic solutions are orbitally stable with respect to subharmonic perturbations of arbitrary period.

nlin.SI↗

arXiv2020

Rogue waves of Ultra-High Peak Amplitude: A Mechanism for Reaching up to Thousand Times the Background Level

We unveil a mechanism enabling a fundamental rogue wave, expressed by a rational function of fourth degree, to reach a peak amplitude as high as a thousand times the background level in a system of coupled nonlinear Schrodinger equations involving both incoherent and coherent coupling terms with suitable coefficients. We obtain the exact explicit vector rational solutions using a Darboux-dressing transformation. We show that both components of such coupled equations can reach extremely high amplitudes. The mechanism is confirmed in direct numerical simulations and its robustness confirmed upon noisy perturbations. Additionally, we showcase the fact that extremely high peak-amplitude vector fundamental rogue waves (of about 80 times the background level) can be excited even within a chaotic background field.

nlin.PS↗