Solutions to the Complex Korteweg-de Vries Equation： Blow-up Solutions and Non-Singular Solutions

In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, includ- ing blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Kort...

Full description

Saved in:
Bibliographic Details
Published inCommunications in theoretical physics Vol. 61; no. 4; pp. 415 - 422
Main Author 孙莹莹 袁渊明 张大军
Format Journal Article
LanguageEnglish
Published 01.04.2014
Subjects
Breathers
Dynamics
Mathematical analysis
Miura变换
Solitons
Theoretical physics
Transformations
公式
孤子解
德弗里斯
方程
溶液
爆破解
非奇异解
Online AccessGet full text
ISSN0253-6102
1572-9494
DOI10.1088/0253-6102/61/4/03

Cover

More Information
Summary:In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, includ- ing blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Korteweg-de Vries equation and a modified Kortcweg-de Vries equation. Using the transformation, solitons, breathers and rational solutions to the com- plex Korteweg-de Vries equation are obtained from those of the modified Korteweg-de Vries equation. Dynamics of the obtained solutions are illustrated.
Bibliography:SUN Ying-Ying, YUAN Juan-Ming and ZHANG Da-Jun （1Department of Mathematics, Shanghai University, Shanghai 200444, China 2Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 433, Taiwan）
blow-up, non-singular solutions, complex Korteweg-de Vries equation
In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, includ- ing blow-up solutions and non-singular solutions. We derive blow-up solutions from known 1-soliton solution and a double-pole solution. There is a complex Miura transformation between the complex Korteweg-de Vries equation and a modified Kortcweg-de Vries equation. Using the transformation, solitons, breathers and rational solutions to the com- plex Korteweg-de Vries equation are obtained from those of the modified Korteweg-de Vries equation. Dynamics of the obtained solutions are illustrated.
11-2592/O3
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0253-6102
1572-9494
DOI:10.1088/0253-6102/61/4/03