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Mathematical Problems in Engineering Volume 2019 ,2019-07-18
Investigation of Interaction Solutions for Modified Korteweg-de Vries Equation by Consistent Riccati Expansion Method
Research Article
Jin-Fu Liang 1 Xun Wang 2
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DOI:10.1155/2019/9535294
Received 2019-03-29, accepted for publication 2019-07-02, Published 2019-07-02
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摘要

A consistent Riccati expansion (CRE) method is proposed for obtaining interaction solutions to the modified Korteweg-de Vries (mKdV) equation. Using the CRE method, it is shown that interaction solutions such as the soliton-tangent (or soliton-cotangent) wave cannot be constructed for the mKdV equation. More importantly, exact soliton-cnoidal periodic wave interaction solutions are presented. While soliton-cnoidal interaction solutions were found to degenerate to special resonant soliton solutions for the values of modulus (n) closer to one (upper bound of modulus) in the Jacobi elliptic function, a normal kink-shaped soliton was observed for values of n closer to zero (lower bound).

授权许可

Copyright © 2019 Jin-Fu Liang and Xun Wang. 2019
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

通讯作者

Jin-Fu Liang.School of Physics and Electronic Science, Guizhou Normal University, Guiyang 550025, China, gznu.edu.cn.liang.shi2007@163.com

推荐引用方式

Jin-Fu Liang,Xun Wang. Investigation of Interaction Solutions for Modified Korteweg-de Vries Equation by Consistent Riccati Expansion Method. Mathematical Problems in Engineering ,Vol.2019(2019)

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