Related papers: Rogue wave pattern of multi-component derivative n…
We present a brief discussion on the nonlinear Schr{\"o}dinger equation for modeling the propagation of the deep-water wavetrains and a discussion on its doubly-localized breather solutions that can be connected to the sudden formation of…
We study fundamental rogue-wave solutions of the focusing nonlinear Schr\"odinger equation in the limit that the order of the rogue wave is large and the independent variables $(x,t)$ are proportional to the order (the far-field limit). We…
In this article we present a new method for construction of exact solutions of the Landau-Lifshitz-Gilbert equation (LLG) for ferromagnetic nanowires. The method is based on the established relationship between the LLG and the nonlinear…
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…
We construct exact soliton solutions of integrable multicomponent nonlinear Schr\"odinger (NLS) equations under general nonvanishing boundary conditions. Different components of the vector (or matrix) dependent variable can approach plane…
Based on modulation instability analysis and generalized Darboux transformation, we derive a hierarchy of rogue wave solutions for a variable-coefficients coupled Hirota equations. The explicit first-order rogue wave solution is presented,…
In this paper, we present a probabilistic study of rare phenomena of the cubic nonlinear Schr\"odinger equation on the torus in a weakly nonlinear setting. This equation has been used as a model to numerically study the formation of rogue…
We present exact rational solution for a modified nonlinear Schr$\ddot{o}$dinger equation that takes into account quintic nonlinearity and nonlinear dispersion corrections to the cubic nonlinearity, which could be used to describe rogue…
We consider the effect of the wind and the dissipation on the nonlinear stages of the modulational instability. By applying a suitable transformation, we map the forced/damped Nonlinear Schr\"odinger (NLS) equation into the standard NLS…
We extend one component Gross-Pitaevskii equation to two component coupled case with the damping term, linear and parabolic density profiles, then give the Lax pair and infinitely-many conservations laws of this coupled system. The system…
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…
Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector…
In this paper, we focus on the two-component (2+1)-dimensional Fokas-Lenells equation, which models the propagation of ultrashort optical pulses in nonlinear media with multi-mode interactions and multi-dimensional effects. Firstly, we…
We consider a coherently coupled nonlinear Schr\"odinger equation with modulated self-phase modulation, cross-phase modulation, and four-wave mixing nonlinearities and varying refractive index in anisotropic graded index nonlinear medium.…
We study a deformation of the nonlinear Schr\"odinger equation recently derived in the context of deformation of hierarchies of integrable systems. This systematic method also led to known integrable equations such as the Camassa-Holm…
We study the applicability of the derivative nonlinear Schr\"{o}dinger (DNLS) equation, for the evolution of high frequency nonlinear waves, observed at the foreshock region of the terrestrial quasi-parallel bow shock. The use of a…
A nonlocal derivative nonlinear Schrodinger equation is introduced. By constructing its basic Darboux transformations of degrees one and two, the explicit expressions of new solutions are derived from seed solutions by Darboux…
In this paper, we consider the complex modified Korteweg-de Vries (mKdV) equation as a model of few-cycle optical pulses. Using the Lax pair, we construct a generalized Darboux transformation and systematically generate the first-, second-…
The Darboux transformation (DT) for the coupled complex short pulse (CCSP) equation is constructed through the loop group method. The DT is then utilized to construct various exact solutions including bright soliton, dark-soliton, breather…
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…