Related papers: Rogue waves in the generalized derivative nonlinea…
We mainly investigate a coupled system of the generalized nonlinear Schr\"odinger equation and the Maxwell-Bloch equations which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order effects including the…
We present a multi-parameter family of rational solutions to the complex Korteweg-de Vries(KdV) equations. This family of solutions includes particular cases with high-amplitude peaks at the centre, as well as a multitude of cases in which…
We report and discuss analytical solutions of the vector nonlinear Schr\"odinger equation that describe rogue waves in the defocusing regime. This family of solutions includes bright-dark and dark-dark rogue waves. The link between…
This paper focuses on the modulation instability, conservation laws and localized wave solutions of the generalized coupled Fokas-Lenells equation. Based on the theory of linear stability analysis, distribution pattern of modulation…
The evolution of unidirectional nonlinear sea surface waves is calculated numerically by means of solutions of the Euler equations. The wave dynamics corresponds to quasi-equilibrium states characterized by JONSWAP spectra. The…
In this work, we consider the dynamics of vector rogue waves and dark-bright solitons in two-component nonlinear Schr\"odinger equations with various physically motivated time-dependent nonlinearity coefficients, as well as…
In this paper we develop a bilinearisation-reduction approach to derive solutions to the classical and nonlocal nonlinear Schr\"{o}dinger (NLS) equations with nonzero backgrounds. We start from the second order Ablowitz-Kaup-Newell-Segur…
The generalized regularized long wave (GRLW) equation has been developed to model a variety of physical phenomena such as ion-acoustic and magnetohydrodynamic waves in plasma, nonlinear transverse waves in shallow water and phonon packets…
Due to the widely applications in almost all branches of science, high dimensional KP equation is selected as universal model to describe rogue wave phenomenon. A lump is an algebraically localized wave decayed in all space directions and…
Dispersive shock waves (DSWs) of the defocusing radial nonlinear Schr\"odinger (rNLS) equation in two spatial dimensions are studied. This equation arises naturally in Bose-Einstein condensates, water waves and nonlinear optics. A unified…
The extreme events are investigated for an $n$-component nonlinear Schr\"odinger ($n$-NLS) system in the focusing Kerr-like nonlinear media, which appears in many physical fields. We report and discuss the novel multi-parametric families of…
We construct the multi-breather solutions of the focusing nonlinear Schr\"odinger equation (NLSE) on the background of elliptic functions by the Darboux transformation, and express them in terms of the determinant of theta functions. The…
The analytical nonautonomous rogons are reported for the inhomogeneous nonlinear Schr\"odinger equation with variable coefficients in terms of rational-like functions by using the similarity transformation and direct ansatz. These obtained…
A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurence of higher-derivative…
We establish universality for extremal solutions of the focusing nonlinear Schr\"{o}dinger equation. Extremal solutions are $N$-soliton solutions that achieve the theoretical maximal amplitude and diverge as $N \to \infty$. We consider…
We have studied the Rogue wave existence and propagation in Ion-acoustic mode for the highly energetic case using kappa distributed electrons in accordance with the Korteweg de Vries equation that is modified KdV and extended KdV equation.…
This work is concerned with the study of explicit solutions for a generalized coupled nonlinear Schr\"{o}dinger equations (NLS) system with variable coefficients. Indeed, we show, employing similarity transformations, the existence of Rogue…
It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless…
Rogue waves (RWs) can form on the ocean surface due to quasi-four wave resonant interaction or superposition principle. Both mechanisms have been acutely studied. The first of the two is known as the nonlinear focusing mechanism and leads…
From among the waves whose dynamics are governed by the nonlinear Schr\"odinger (NLS) equation, we find a robust, spatiotemporally disordered family, in which waves initialized with increasing amplitudes, on average, over long time scales,…