An explicit expression of the dark N-soliton solution of the MKdV equation by means of the Darboux transformation

1993 ◽  
Vol 26 (6) ◽  
pp. 1365-1374 ◽  
Author(s):  
Zong-Yun Chen ◽  
Nian-Ning Huang ◽  
Zhong-Zhu Liu ◽  
Yi Xiao
Keyword(s):  
Explicit Expression ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Mkdv Equation

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.

DETERMINANT REPRESENTATION OF N-TIMES DARBOUX TRANSFORMATION FOR THE DEFOCUSING NONLINEAR SCHRÖDINGER EQUATION

2013 ◽  
Vol 27 (29) ◽  
pp. 1350216 ◽  
Author(s):  
JINGWEI HAN ◽  
JING YU ◽  
JINGSONG HE
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nls Equation ◽  
Nonlinear Schrödinger ◽  
Determinant Representation

The determinant expression T[N] of a new Darboux transformation (DT) for the Ablowitz–Kaup–Newell–Segur equation are given in this paper. By making use of this DT under the reduction r = q*, we construct determinant expressions of dark N-soliton solution for the defocusing NLS equation. Except known one-soliton, we provide smooth two-soliton and smooth N-soliton on a certain domain of parameter for the defocusing NLS equation.

Darboux transformation and analytic solutions for a generalized super-NLS-mKdV equation

2019 ◽  
Vol 98 (2) ◽  
pp. 1491-1500 ◽  
Author(s):  
Xue Guan ◽  
Wenjun Liu ◽  
Qin Zhou ◽  
Anjan Biswas
Keyword(s):  
Darboux Transformation ◽  
Analytic Solutions ◽  
Mkdv Equation

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 .

scholarly journals Darboux transformation and exact solutions of the integrable Heisenberg ferromagnetic equation with self-consistent potentials

2016 ◽  
Vol 13 (01) ◽  
pp. 1550134 ◽  
Author(s):  
Z. S. Yersultanova ◽  
M. Zhassybayeva ◽  
K. Yesmakhanova ◽  
G. Nugmanova ◽  
R. Myrzakulov
Keyword(s):  
Exact Solutions ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Integrable Systems ◽  
Self Consistent

Integrable Heisenberg ferromagnetic equations are an important subclass of integrable systems. The M-XCIX equation is one of a generalizations of the Heisenberg ferromagnetic equation and are integrable. In this paper, the Darboux transformation of the M-XCIX equation is constructed. Using the DT, a 1-soliton solution of the M-XCIX equation is presented.

DARBOUX TRANSFORMATION OF THE MODIFIED TODA LATTICE EQUATION

2006 ◽  
Vol 20 (11) ◽  
pp. 641-648 ◽  
Author(s):  
XI-XIANG XU ◽  
HONG-XIANG YANG ◽  
YE-PENG SUN
Keyword(s):  
Spectral Problem ◽  
Soliton Solution ◽  
Darboux Transformation ◽  
Toda Lattice ◽  
Lattice Equation ◽  
Matrix Spectral Problem ◽  
Toda Lattice Equation

A modified Toda lattice equation associated with a properly discrete matrix spectral problem is introduced. Darboux transformation for the resulting lattice equation is constructed. As an application, the soliton solution for the Toda lattice equation is explicitly given.

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