KdV Equation with Self-consistent Sources in Non-uniform Media

2009 ◽  
Vol 51 (6) ◽  
pp. 989-999 ◽  
Author(s):  
Hao Hong-Hai ◽  
Wang Guang-Sheng ◽  
Zhang Da-Jun
Keyword(s):  
Kdv Equation ◽  
Self Consistent

scholarly journals On the Integration of the matrix modified Korteweg-de Vries equation with a self-consistent source

2019 ◽  
Vol 50 (3) ◽  
pp. 281-291 ◽  
Author(s):  
G. U. Urazboev ◽  
A. K. Babadjanova
Keyword(s):  
Vries Equation ◽  
Kdv Equation ◽  
Scattering Data ◽  
Self Consistent ◽  
De Vries ◽  
The Matrix

In this work we deduce laws of the evolution of the scattering  data for the matrix Zakharov Shabat system with the potential that is the solution of the matrix modied KdV equation with a self consistent source.

Integration of the matrix KdV equation with self-consistent source

2013 ◽  
Vol 49 ◽  
pp. 21-27 ◽  
Author(s):  
N. Bondarenko ◽  
G. Freiling ◽  
G. Urazboev
Keyword(s):  
Kdv Equation ◽  
Self Consistent ◽  
The Matrix

scholarly journals Solutions and Painlevé Property for the KdV Equation with Self-Consistent Source

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Yali Shen ◽  
Ruoxia Yao
Keyword(s):  
Kdv Equation ◽  
Traveling Wave Solutions ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Hyperbolic Function ◽  
Group Invariant ◽  
Painlevé Property ◽  
The Kdv Equation ◽  
Self Consistent ◽  
Group Invariant Solutions

In this paper, the polynomial solutions in terms of Jacobi’s elliptic functions of the KdV equation with a self-consistent source (KdV-SCS) are presented. The extended (G′/G)-expansion method is utilized to obtain exact traveling wave solutions of the KdV-SCS, which finally are expressed in terms of the hyperbolic function, the trigonometric function, and the rational function. Meanwhile we find the Lie point symmetry and Lie symmetry group and give several group-invariant solutions for the KdV-SCS. Finally, we supplement the results of the Painlevé property in our previous work and get the Bäcklund transformations of the KdV-SCS.

The periodic solutions of the discrete modified KdV equation with a self-consistent source

2020 ◽  
Vol 376 ◽  
pp. 125136
Author(s):  
Aygul Babadjanova ◽  
Thomas Kriecherbauer ◽  
Gayrat Urazboev
Keyword(s):  
Periodic Solutions ◽  
Kdv Equation ◽  
Modified Kdv Equation ◽  
Self Consistent

scholarly journals The Painlevé Tests, Bäcklund Transformation and Bilinear Form for the KdV Equation with a Self-Consistent Source

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Yali Shen ◽  
Fengqin Zhang ◽  
Xiaomei Feng
Keyword(s):  
Soliton Solution ◽  
Bilinear Form ◽  
Bäcklund Transformation ◽  
Kdv Equation ◽  
Bilinear Operator ◽  
Backlund Transformation ◽  
Painlevé Property ◽  
Bilinear Bäcklund Transformation ◽  
The Kdv Equation ◽  
Self Consistent

The Painlevé property and Bäcklund transformation for the KdV equation with a self-consistent source are presented. By testing the equation, it is shown that the equation has the Painlevé property. In order to further prove its integrality, we give its bilinear form and construct its bilinear Bäcklund transformation by the Hirota's bilinear operator. And then the soliton solution of the equation is obtained, based on the proposed bilinear form.

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