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Generalised (2+1)-dimensional Super MKdV Hierarchy for Integrable Systems in Soliton Theory

Published online by Cambridge University Press:  07 September 2015

Huanhe Dong ,
Kun Zhao ,
Hongwei Yang  and
Yuqing Li
Huanhe Dong
Affiliation:
College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China
Kun Zhao*
Affiliation:
College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China
Hongwei Yang
Affiliation:
College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China
Yuqing Li
Affiliation:
College of Mathematics and System Science, Shandong University of Science and Technology, Qingdao 266590, China
*
*Corresponding author. Email address: [email protected] (K. Zhao)
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Abstract

Much attention has been given to constructing Lie and Lie superalgebra for integrable systems in soliton theory, which often have significant scientific applications. However, this has mostly been confined to (1+1)-dimensional integrable systems, and there has been very little work on (2+1)-dimensional integrable systems. In this article, we construct a class of generalised Lie superalgebra that differs from more common Lie superalgebra to generate a (2+1)-dimensional super modified Korteweg-de Vries (mKdV) hierarchy, via a generalised Tu scheme based on the Lax pair method where the Hamiltonian structure derives from a generalised supertrace identity. We also obtain some solutions of the (2+1)-dimensional mKdV equation using the G′/G2 method.

Keywords

35Q5137K0537K10Soliton theorygeneralised Lie superalgebra, (2+1)-dimensional super mKdV hierarchysupertrace identity, G′/G2 method
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 5 , Issue 3 , August 2015 , pp. 256 - 272
Copyright
Copyright © Global-Science Press 2015 

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