Related papers: Nonlinear Schr\"odinger Equation: Generalized Darb…
The Hirota equation is an integrable higher order nonlinear Schr\"{o}dinger type equation which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for the Hirota equation and…
In this letter,the designable integrability(DI) of the variable coefficient derivative nonlinear Schr\"odinger equation (VCDNLSE) is shown by construction of an explicit transformation which maps VCDNLSE to the usual derivative nonlinear…
We introduce a new, more general type of nonlinear gauge transformation in nonrelativistic quantum mechanics that involves derivatives of the wave function and belongs to the class of B\"acklund transformations. These transformations…
In this work, we focus on the construction of Nth-rouge wave solutions for the Hirota equation by utilizing the bilinear method. The formula can be represented in terms of determinants. In addition, some interesting dynamic patterns of…
The Sasa-Satsuma equation is an integrable higher-order nonlinear Schr\"odinger equation. Higher-order and multicomponent generalisations of the nonlinear Schr\"odinger equation are important in various applications, e.g., in optics. One of…
We consider the kinetic derivative nonlinear Schr\"odinger equation, which is a one-dimensional nonlinear Schr\"odinger equation with a cubic derivative nonlinear term containing the Hilbert transformation. In our previous work, we proved…
We investigate the reduced Maxwell-Bloch (RMB) equations which describe the propagation of short optical pulses in dielectric materials with resonant non-degenerate transitions. The general Nth-order periodic solutions are provided by means…
By employing a mapping to classical anharmonic oscillators, we explore a class of solutions to the Nonlinear Schrodinger Equation (NLSE) in 1+1 dimensions and, by extension, asymptotically in general dimensions. We discuss a possible way…
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,…
The Darboux--Dressing Transformations are applied to the Lax pair associated to the system of nonlinear equations describing the resonant interaction of three waves in 1+1 dimensions. We display explicit solutions featuring localized waves…
The Hirota equation is a higher order extension of the nonlinear Schroedinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of…
We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schr\"{o}dinger equations. We find four fundamental rogue waves can emerge for second-order vector RW in the coupled system, in contrast to the high-order ones…
We consider the high-order nonlinear Schr\"odinger equation derived earlier by Sedletsky [Ukr. J. Phys. 48(1), 82 (2003)] for the first-harmonic envelope of slowly modulated gravity waves on the surface of finite-depth irrotational,…
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 plane wave solutions of the three-wave resonant interaction in the plane are considered. It is shown that rank-one constraints over the right derivatives of invertible operators on an arbitrary linear space gives solutions of the…
Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr\"odinger equations with potentials and nonlinearities depending on time and on the spatial coordinates. We present the general theory and use it…
Considering certain terms of the next asymptotic order beyond the nonlinear Schrodinger equation (NLS) equation, the Fokas-Lenells (FL) equation governed by the FL system arise as a model for nonlinear pulse propagation in optical fibers.…
Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schr\"odinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general…
Considering the importance of ever-increasing interest in exploring localized waves, we investigate a generalized (3+1)-dimensional Hirota-Satsuma-Ito equation describing the unidirectional propagation of shallow-water waves and perform…
A recent development in the derivation of soliton solutions for initial-boundary value problems through Darboux transformations, motivated to reconsider solutions to the nonlinear Schr\"odinger (NLS) equation on two half-lines connected via…