Explicit solution and Darboux transformation for a new discrete integrable soliton hierarchy with 4×4 Lax pairs

2017 ◽  
Vol 40 (15) ◽  
pp. 5515-5525 ◽  
Author(s):  
Fajun yu ◽  
Shuo Feng
Keyword(s):  
Darboux Transformation ◽  
Explicit Solution ◽  
Lax Pairs ◽  
Soliton Hierarchy

scholarly journals N-Fold Darboux Transformation for the Classical Three-Component Nonlinear Schrödinger Equations and Its Exact Solutions

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 733
Author(s):  
Yu-Shan Bai ◽  
Peng-Xiang Su ◽  
Wen-Xiu Ma
Keyword(s):  
Exact Solutions ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Lax Pairs ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrodinger Equations ◽  
The Given

In this paper, by using the gauge transformation and the Lax pairs, the N-fold Darboux transformation (DT) of the classical three-component nonlinear Schrödinger (NLS) equations is given. In addition, by taking seed solutions and using the DT, exact solutions for the given NLS equations are constructed.

INTEGRABLE COUPLINGS FOR THE ABLOWITZ–LADIK LATTICE THROUGH ENLARGING ASSOCIATED LAX PAIRS

2006 ◽  
Vol 20 (05) ◽  
pp. 253-259
Author(s):  
NING ZHANG ◽  
XI-XIANG XU ◽  
HONG-XIANG YANG
Keyword(s):  
Discrete Systems ◽  
Lax Pairs ◽  
Spectral Problems ◽  
Soliton Hierarchy ◽  
Integrable Couplings

A direct way to construct integrable couplings for discrete systems is introduced through enlarging associated spectral problems. As an application, the procedure for the Ablowitz–Ladik lattice soliton hierarchy is employed.

scholarly journals A Five-Component Generalized mKdV Equation and Its Exact Solutions

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1145
Author(s):  
Bo Xue ◽  
Huiling Du ◽  
Ruomeng Li
Keyword(s):  
Exact Solutions ◽  
Spectral Problem ◽  
Darboux Transformation ◽  
Rational Functions ◽  
Mkdv Equation ◽  
Darboux Transformations ◽  
Lax Pairs ◽  
Gauge Transformations

In this paper, a 3 × 3 spectral problem is proposed and a five-component equation that consists of two different mKdV equations is derived. A Darboux transformation of the five-component equation is presented relating to the gauge transformations between the Lax pairs. As applications of the Darboux transformations, interesting exact solutions, including soliton-like solutions and a solution that consists of rational functions of e x and t, for the five-component equation are obtained.

scholarly journals Binary non-linearization of Lax pairs of Kaup-Newell soliton hierarchy

1996 ◽  
Vol 111 (9) ◽  
pp. 1135-1149 ◽  
Author(s):  
W. -X. Ma ◽  
Q. Ding ◽  
W. G. Zhang ◽  
B. Q. Lu
Keyword(s):  
Lax Pairs ◽  
Soliton Hierarchy

scholarly journals On the continuum limit for a semidiscrete Hirota equation

2016 ◽  
Vol 472 (2195) ◽  
pp. 20160628 ◽  
Author(s):  
Andrew Pickering ◽  
Hai-qiong Zhao ◽  
Zuo-nong Zhu
Keyword(s):  
Soliton Solution ◽  
Darboux Transformation ◽  
Explicit Solution ◽  
Continuum Limit ◽  
Lax Pair ◽  
Discrete Space ◽  
Hirota Equation ◽  
Space Step ◽  
The Continuum

In this paper, we propose a new semidiscrete Hirota equation which yields the Hirota equation in the continuum limit. We focus on the topic of how the discrete space step δ affects the simulation for the soliton solution to the Hirota equation. The Darboux transformation and explicit solution for the semidiscrete Hirota equation are constructed. We show that the continuum limit for the semidiscrete Hirota equation, including the Lax pair, the Darboux transformation and the explicit solution, yields the corresponding results for the Hirota equation as δ → 0 .

THE GENERALIZED MULTI-COMPONENT AKNS HIERARCHY AND N-FOLD DARBOUX TRANSFORMATION

2006 ◽  
Vol 20 (25) ◽  
pp. 1575-1589 ◽  
Author(s):  
HONG-XIANG YANG ◽  
DAO-LIN WANG ◽  
CHANG-SHENG LI
Keyword(s):  
Spectral Problem ◽  
Darboux Transformation ◽  
Soliton Solutions ◽  
Soliton Equation ◽  
Lax Pairs ◽  
Akns Hierarchy ◽  
Soliton Equations ◽  
Gauge Transformations ◽  
Set Up ◽  
Liouville Integrable

Starting from a 3×3 spectral problem, by using the Tu scheme, a hierarchy of generalized multi-component AKNS soliton equations are derived. It is shown that each equation in the resulting hierarchy is Liouville integrable. With the help of gauge transformations of the Lax pairs, an N-fold Darboux transformation (DT) with multi-parameters for the spectral problem is set up. For application, the soliton solutions of the first nonlinear soliton equation are explicitly given.

Sign in / Sign up

Export Citation Format

Share Document