Year: 2015
East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 3 : pp. 256–272
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 $G′/G^{2}$ method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.110215.010815a
East Asian Journal on Applied Mathematics, Vol. 5 (2015), Iss. 3 : pp. 256–272
Published online: 2015-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Soliton theory generalised Lie superalgebra (2+1)-dimensional super mKdV hierarchy supertrace identity $G′/G^{2}$ method.