Related papers: Darboux transformation and soliton solutions of th…
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…
In this paper, we propose a complex short pulse equation of both focusing and defocusing types, which governs the propagation of ultra-short pulses in nonlinear optical fibers. It can be viewed as an analogue of the nonlinear Schr\"odinger…
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…
Darboux transformation is one of the methods used in solving nonlinear evolution equation. Basically, the Darboux transformation is a linear algebra formulation of the solutions of the Zakharov-Shabat system of equations associated with the…
In this paper, we investigate the nonlocal generalized Sasa-Satsuma (ngSS) equation based on an improved Riemann-Hilbert method (RHM). Different from the traditional RHM, the $t$-part of the Lax pair plays a more important role rather than…
In this paper, we primarily construct Darboux transformation(DT) of the nonlocal coupled modified complex integrable dispersionless (cm-CID) equation, which is first proposed by the connection with a nonlocal coupled modified complex short…
We derive generalized nonlinear wave solution formula for mixed coupled nonlinear Sch\"odinger equations (mCNLSE) by performing the unified Darboux transformation. We give the classification of the general soliton formula on the nonzero…
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 study a discrete Darboux transformation and construct the multi-soliton solutions in terms of ratio of determinants for integrable discrete sine-Gordon equation. We also calculate explicit expressions of single, double, triple, quad…
The second-type derivative nonlinear Schr\"odinger (DNLSII) equation was introduced as an integrable model in 1979. Very recently, the DNLSII equation has been shown by an experiment to be a model of the evolution of optical pulses…
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 construct the generalized Darboux transformation with arbitrary functions in time $t$ for the AKNS equation with self-consistent sources (AKNSESCS) which, in contrast with the Darboux transformation for the AKNS equation, provides a…
Higher order and multicomponent generalizations of the nonlinear Schrodinger equation are important in various applications, e.g., in optics. One of these equations, the integrable Sasa-Satsuma equation, has particularly interesting soliton…
In this article, a fully discrete short pulse (SP) equation is presented as an integrability condition of a linear system of difference equations (also known as discrete Lax pair). Additionally, two semi-discrete versions of the SP equation…
In this paper, we investigate smooth positon and breather-positon solutions of a generalized nonlinear Schr\"{o}dinger (GNLS) equation which contains higher order nonlinear effects. With the help of generalized Darboux transformation (GDT)…
In this letter, via the Darboux transformation method we construct new analytic soliton solutions for the Sasa-Satsuma equation which describes the femtosecond pulses propagation in a monomode fiber. We reveal that two different types of…
In this paper, the Darboux transformation (DT) of the reverse space-time (RST) nonlocal short pulse equation is constructed by a hodograph transformation and the eigenfunctions of its Lax pair. The multi-soliton solutions of the RST…
In this paper, we construct a generalized Darboux transformation for nonlinear Schr\"odinger equation. The associated $N$-fold Darboux transformation is given both in terms of a summation formula and in terms of determinants. As…
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…
In this letter, for the discrete parity-time-symmetric nonlocal nonlinear Schr\"{o}dinger equation, we construct the Darboux transformation, which provides an algebraic iterative algorithm to obtain a series of analytic solutions from a…