相关论文: Stable multicolor periodic-wave arrays

We numerically investigate transverse stability and instability of so-called cnoidal waves, i.e., periodic traveling wave solutions of the Korteweg-de Vries equation, under the time-evolution of the Kadomtsev-Petviashvili equation. In…

Conditions for stable propagation of one-dimensional bright spatial solitons in media exhibiting optical nonlinearities up to the seventh-order are investigated. The results show well-defined stability regions even when all the nonlinear…

In this paper, we prove existence and orbital stability results of periodic standing waves for the cubic-quintic nonlinear Schr\"odinger equation. We use the implicit function theorem to construct a smooth curve of explicit periodic waves…

We study the spectral stability properties of periodic traveling waves in the sine-Gordon equation, including waves of both subluminal and superluminal propagation velocities as well as waves of both librational and rotational types. We…

We prove the orbital stability of periodic traveling-wave solutions for systems of dispersive equations with coupled nonlinear terms. Our method is basically developed under two assumptions: one concerning the spectrum of the linearized…

We consider reaction-diffusion systems with multiplicative noise on a spatial domain of dimension two or higher. The noise process is white in time, coloured in space, and invariant under translations. In the deterministic setting,…

We study the propagation of ultra-short pulses in a cubic nonlinear medium. Using multiple-scale technique, we derive a new wave equation that preserves the nonlocal dispersion present in Maxwell's equations. As a result, we are able to…

In this work, we present a numerical study of the wave stability of steady solitary waves over a localised topographic obstacle through the full Euler equations. There are two branches of the solutions: one from the perturbed uniform flow…

This paper establishes suficient conditions for the orbital stability of one-parameter spatially periodic traveling-wave solutions for one-dimensional dispersive equations. Our method of proof combines known techniques with some new ideas.…

This manuscript investigates the existence and spectral stability of multiple periodic standing wave solutions for a nonlinear Schr\"odinger system. By considering both cnoidal and snoidal profiles, we provide a comprehensive spectral…

Single solitons are a special limit of more general waveforms commonly referred to as cnoidal waves or Turing rolls. We theoretically and computationally investigate the stability and accessibility of cnoidal waves in microresonators. We…

We study standing periodic waves modeled by the nonlinear Schrodinger equation with the intensity-dependent dispersion coefficient. Spatial periodic profiles are smooth if the frequency of the standing waves is below the limiting frequency,…

Early results concerning the shape and stability of ion acoustic waves are generalized to propagation at an angle to the magnetic field lines. Each wave has a critical angle for stability. Known soliton results are recovered as special…

We develop a stability theory for two-dimensional periodic traveling waves of general parabolic systems, possibly including conservation laws. In particular, we identify a diffusive spectral stability assumption and prove that it implies…

In this paper, we study the orbital stability of standing waves for one-dimensional nonlinear Schr\"odinger equations with potentials. We show that the standing waves are orbitally stable for all frequencies in the $L^{2}$- subcritical and…

In this note, we extend the detailed study of the linearized dynamics obtained for cnoidal waves of the Korteweg--de Vries equation in \cite{JFA-R} to small-amplitude periodic traveling waves of the generalized Korteweg-de Vries equations…

We demonstrate the existence of stable three-dimensional spatiotemporal solitons (STSs) in media with a nonlocal cubic nonlinearity. Fundamental (nonspinning) STSs forming one-parameter families are stable if their propagation constant…

The quasi-one-dimensional rhombic array of the waveguides is considered. In the nonlinear case the system of equations describing coupled waves in the waveguides has the solutions that represent the superposition of the flat band modes. The…

The stability of two-dimensional bright vortex solitons in a media with focusing cubic and defocusing quintic nonlinearities is investigated analytically and numerically. It is proved that above some critical beam powers not only one- and…

We study the propagation of femtosecond light pulses inside an optical fiber medium exhibiting higher-order dispersion and cubic-quintic nonlinearities. Pulse evolution in such system is governed by a higher-order nonlinear Schr%…