Related papers: Nonlinear Schr\"odinger Equation: Generalized Darb…
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…
In the present investigation, the solutions on the periodic and double-periodic background are successfully constructed by Darboux transformation using a plane wave seed solution. Firstly, the Darboux transformation for the…
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…
The height of an $n$th-order fundamental rogue wave $q_{\rm rw}^{[n]}$ for the nonlinear Schr\"odinger equation, namely $(2n+1)c$, is proved directly by a series of row operations on matrices appeared in the $n$-fold Darboux transformation.…
In this paper, we provide a simple method to generate higher order position solutions and rogue wave solutions for the derivative nonlinear Schr\"odinger equation. The formulae of these higher order solutions are given in terms of…
In this article, we derive rogue wave (RW) solutions of a fifth-order nonlinear Schr\"odinger equation over a double-periodic wave background. Choosing the elliptic functions (combinations of $cn$, $dn$ and $sn$) as seed solutions in the…
The Hirota equation is better than the nonlinear Schr\"{o}dinger equation when approximating deep ocean waves. In this paper, high-order rational solutions for the Hirota equation are constructed based on the parameterized Darboux…
In this paper, the generalized Darboux transformation is established to the AB system, which mainly describes marginally unstable baroclinic wave packets in geophysical fluids and ultra-short pulses in nonlinear optics. We find a unified…
Modulation instability, rogue wave and spectral analysis are investigated for the nonlinear Schrodinger equation with the higher-order terms. The modulation instability distribution characteristics from the sixth-order to the eighth-order…
In the present paper, we are concerned with the general localized solutions for the complex short pulse equation including soliton, breather and rogue wave solutions. With the aid of a generalized Darboux transformation, we construct the…
We construct rogue wave solutions of a fifth-order nonlinear Schr\"odinger equation on the Jacobian elliptic function background. By combining Darboux transformation and the nonlinearization of spectral problem, we generate rogue wave…
In this paper, we consider the two component derivative nonlinear Schr\"{o}dinger equation and present a simple Darboux transformation for it. By iterating this Darboux transformation, we construct a compact representation for the…
The nonlocal Darboux transformation of the stationary axially symmetric Schr\"odinger equation is considered. It is shown that a special case of the nonlocal Darboux transformation provides the generalization of the Moutard transformation.…
This paper is devoted to a comprehensive analysis of a family of solutions of the focusing nonlinear Schr\"odinger equation called general rogue waves of infinite order. These solutions have recently been shown to describe various limit…
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 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…
We construct certain higher order smooth positon and breather positon solutions of an extended nonlinear Schr\"odinger equation with the cubic and quartic nonlinearity. We utilize the generalized Darboux transformation method to construct…
In this paper, general higher-order rogue wave solutions of the parity-time ($\mathcal {P}\mathcal {T}$) symmetric scalar and coupled nonlocal nonlinear Schr\"{o}dinger equations (NLSEs) are calculated theoretically via a Darboux…
We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schr\"odinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, and…
We construct Darboux transformation of a coupled generalized nonlinear Schr\"odinger (CGNLS) equations and obtain exact analytic expressions of breather and rogue wave solutions. We also formulate the conditions for isolating these…