scholarly journals Darboux transformation and soliton solution for the (2+1)-dimensional complex modified Korteweg-de Vries equations

2017 ◽  
Vol 936 ◽  
pp. 012045 ◽  
Author(s):  
K Yesmakhanova ◽  
G Shaikhova ◽  
G Bekova ◽  
R Myrzakulov
Keyword(s):  
Soliton Solution ◽  
Darboux Transformation ◽  
De Vries

scholarly journals Construction of Higher-Order Smooth Positons and Breather Positons via Hirota's Bilinear Method

2021 ◽  
Author(s):  
Zhao Zhang ◽  
Biao Li ◽  
Junchao Chen ◽  
QI GUO
Keyword(s):  
Soliton Solution ◽  
Darboux Transformation ◽  
Mathematical Expression ◽  
Higher Order ◽  
Second Order ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Advantages And Disadvantages ◽  
De Vries ◽  
Generalized Darboux Transformation

Abstract Based on the Hirota's bilinear method, a more classic limit technique is perfected to obtain second-order smooth positons. Immediately afterwards, we propose an extremely ingenious limit approach in which higher-order smooth positons and breather positons can be quickly derived from N-soliton solution. Under this ingenious technique, the smooth positons and breather positons of the modified Korteweg-de Vries system are quickly and easily derived. Compared with the generalized Darboux transformation, the approach mentioned in this paper has the following advantages and disadvantages: the advantage is that it is simple and fast; the disadvantage is that this method cannot get a concise general mathematical expression of nth-order smooth positons.

THE SECOND-ORDER KdV EQUATION AND ITS SOLITON-LIKE SOLUTION

2009 ◽  
Vol 23 (14) ◽  
pp. 1771-1780 ◽  
Author(s):  
CHUN-TE LEE ◽  
JINN-LIANG LIU ◽  
CHUN-CHE LEE ◽  
YAW-HONG KANG
Keyword(s):  
Solitary Waves ◽  
Soliton Solution ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Second Order ◽  
Close Resemblance ◽  
De Vries

This paper presents both the theoretical and numerical explanations for the existence of a two-soliton solution for a second-order Korteweg-de Vries (KdV) equation. Our results show that there exists "quasi-soliton" solutions for the equation in which solitary waves almost retain their identities in a suitable physical regime after they interact, and bear a close resemblance to the pure KdV solitons.

Decomposition, Darboux transformation and soliton solutions for the (2 + 1)-dimensional integrable nonlocal “breaking soliton” equation

2020 ◽  
Vol 34 (24) ◽  
pp. 2050251
Author(s):  
Xiaoming Zhu ◽  
Kelei Tian
Keyword(s):  
Darboux Transformation ◽  
Schrodinger Equation ◽  
Vries Equation ◽  
Soliton Solutions ◽  
Soliton Equation ◽  
Interaction Mechanisms ◽  
Dark Solitons ◽  
De Vries ◽  
Nonlocal Nonlinear Schrödinger Equation ◽  
Nonlocal Nonlinear

In this paper, we investigate an integrable nonlocal “breaking soliton” equation, which can be decomposed into the nonlocal nonlinear Schrödinger equation and the nonlocal complex modified Korteweg–de Vries equation. As an application, with the use of this decomposition and Darboux transformation, the dark solitons, antidark solitons, rational dark solitons and rational antidark solitons of the considered equation are given explicitly. In particular, the interaction mechanisms of these solutions are discussed and illustrated through some figures.

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.

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