Related papers: Dark solitons, dispersive shock waves, and transve…
We obtain sharp criteria for transverse stability and instability of line solitons in the discrete nonlinear Schr\"{o}dinger equations on one- and two-dimensional lattices near the anti-continuum limit. On a two-dimensional lattice, the…
The spatially periodic breather solutions (SPBs) of the nonlinear Schr\"odinger equation, prominent in modeling rogue waves, are unstable. In this paper we numerically investigate the effects of nonlinear dissipation and higher order…
We consider the statics and dynamics of dark matter-wave solitons in the dimensionality crossover regime from 3D to 1D. There, using the nonpolynomial Schr\"{o}dinger mean-field model, we find that the anomalous mode of the Bogoliubov…
In this work, we study solitary waves in a (2+1)-dimensional variant of the defocusing nonlinear Schr\"odinger (NLS) equation, the so-called Camassa-Holm NLS (CH-NLS) equation. We use asymptotic multiscale expansion methods to reduce this…
The dynamics of dark matter-wave solitons in elongated atomic condensates are discussed at finite temperatures. Simulations with the stochastic Gross-Pitaevskii equation reveal a noticeable, experimentally observable spread in individual…
We consider KdV-type equations with $C^1$ nonhomogeneous nonlinearities and small dispersion $\varepsilon$. The first result consists in the conclusion that, in the leading term with respect to $\varepsilon$, the solitary waves in this…
We study dynamics of dark solitons in the theory of the DNLS equation by the method based on imposing the condition that this dynamics must be Hamiltonian. Combining this condition with Stokes' remark that relationships for harmonic linear…
We prove nonlinear modulational instability for both periodic and localized perturbations of periodic traveling waves for several dispersive PDEs, including the KDV type equations (e.g. the Whitham equation, the generalized KDV equation,…
We analyze the Drinfeld-Sokolob-Wilson system, which features a dispersive, KdV type evolution with a dispersionless conservation law. We establish well-posedness with low regularity initial data $L^2({\mathbb T})\times L^2({\mathbb T})$…
We study a class of 1+1 quadratically nonlinear water wave equations that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still preserves…
The Hyperbolic Nonlinear Schrodinger equation (HypNLS) arises as a model for the dynamics of three-dimensional narrowband deep water gravity waves. In this study, the Petviashvili method is exploited to numerically compute bi-periodic…
We determine the nonlinear stability of shock-fronted travelling waves arising in a reaction-nonlinear diffusion PDE, subject to a fourth-order spatial derivative term multiplied by a small parameter $\varepsilon$ that models {\it nonlocal…
Rogue waves are abnormally large waves which appear unexpectedly and have attracted considerable attention, particularly in recent years. The one space, one time (1+1) nonlinear Schr\"odinger equation is often used to model rogue waves; it…
The effect of the modulation instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schr\"odinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed…
Sardar et al. [Phys. Plasmas 23, 073703 (2016)] have studied the stability of small amplitude dust ion acoustic solitary waves in a collisionless unmagnetized electron - positron - ion - dust plasma. They have derived a Kadomtsev…
This article investigates the qualitative aspects of dark solitons of one-dimensional Gross-Pitaevskii equations with general nonlocal interactions, which correspond to traveling waves with subsonic speeds. Under general conditions on the…
We consider the problem of existence and stability of solitary traveling waves for the one dimensional discrete non linear Schroedinger equation (DNLS) with cubic nonlinearity, near the continuous limit.We construct a family of solutions…
Full dispersive models of water waves, such as the Whitham equation and the full dispersion Kadomtsev-Petviashvili (KP) equation, are interesting from both the physical and mathematical points of view. This paper studies analogous full…
The Camassa-Holm-Kadomtsev-Petviashvili-I equation (CH-KP-I) is a two dimensional generalization of the Camassa-Holm equation (CH). In this paper, we prove transverse instability of the line solitary waves under periodic transverse…
We study the propagation of narrow solitons through various profiles of dispersive shock waves (DSW) for the generalized Korteweg-de Vries equation. We consider situations in which the soliton passes through the DSW region quickly enough…