Related papers: On Rogue wave in the Kundu-DNLS equation
The long wave-short wave model describes the interaction between the long wave and the short wave. Exact higher-order rational solution expressed by determinants is calculated via the Hirota's bilinear method and the KP hierarchy reduction.…
We report new rogue wave patterns in the nonlinear Schr\"{o}dinger equation. These patterns include heart-shaped structures, fan-shaped sectors, and many others, that are formed by individual Peregrine waves. They appear when multiple…
A new exactly solvable (1+1)-dimensional complex nonlinear wave equation exhibiting rich ana- lytic properties has been introduced. A rogue wave (RW), localized in space-time like Peregrine RW solution, though richer due to the presence of…
In this paper, general rogue wave solutions in the massive Thirring (MT) model are derived by using the Kadomtsev-Petviashvili (KP) hierarchy reduction method and these rational solutions are presented explicitly in terms of determinants…
In this work, we construct various interesting localized wave structures of the Benjamin-Ono equation describing the dynamics of deep water waves. Particularly, we extract the rogue waves and generalized breather solutions with the aid of…
The higher-order dispersive and nonlinear effects (alias {\it the perturbation terms}) like the third-order dispersion, the self-steepening, and the self-frequency shift play important roles in the study of the ultra-short optical pulse…
In the present work, a nonlocal nonlinear Schr\"odinger (NLS) model is studied by means of a recent technique that identifies solutions of partial differential equations, by considering them as fixed points in {\it space-time}. This…
We measure evolution of spectra, spatial correlation functions and probability density functions (PDFs) of waves appearance for a set of one-dimensional NLS-like equations of focusing type, namely for the classical integrable Nonlinear…
The integrable nonlocal nonlinear Schrodinger (NNLS) equation with the self-induced parity-time-symmetric potential [Phys. Rev. Lett. 110 (2013) 064105] is investigated, which is an integrable extension of the standard NLS equation. Its…
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…
This paper investigates a reverse space-time higher-order modified self-steepening nonlinear Schr\"odinger equation, which distinguishes its standard local counterparts through the reverse space-time symmetry. The integrability of this…
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…
In this paper, we obtain a uniform Darboux transformation for multi-component coupled NLS equations, which can be reduced to all previous presented Darboux transformation. As a direct application, we derive the single dark soliton and…
An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schr\"{o}dinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the…
By means of certain limit technique, two kinds of generalized Darboux transformations are constructed for the derivative nonlinear Sch\"odinger equation (DNLS). These transformations are shown to lead to two solution formulas for DNLS in…
We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schr\"odinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe…
The nonlinear Schrodinger equation is a classical integrable equation which contains plenty of significant properties and occurs in many physical areas. However, due to the difficulty of solving this equation, in particular in high…
We construct vector rogue wave solutions of the two-dimensional two coupled nonlinear Schr\"{o}dinger equations with distributed coefficients, namely diffraction, nonlinearity and gain parameters through similarity transformation technique.…
We present a new exact solution to the defocusing modified Korteweg-de Vries equation to describe the interaction of a dark soliton and a traveling periodic wave. The solution (which we refer to as to the dark breather) is obtained by using…
We investigate the nonisospectral effects of a semi-discrete nonlinear Schr\"{o}dinger equation, which is a direct integrable discretisation of its continuous counterpart. Bilinear form and double casoratian solution of the equation are…