Volume 5, Issue 3
Generalised (2+1)-Dimensional Super MKdV Hierarchy for Integrable Systems in Soliton Theory

East Asian J. Appl. Math., 5 (2015), pp. 256-272.

Published online: 2018-02

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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 $G′/G^{2}$ method.

• Keywords

Soliton theory, generalised Lie superalgebra, (2+1)-dimensional super mKdV hierarchy, supertrace identity, $G′/G^{2}$ method.

35Q51, 37K05, 37K10

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• RIS
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@Article{EAJAM-5-256, author = {}, title = {Generalised (2+1)-Dimensional Super MKdV Hierarchy for Integrable Systems in Soliton Theory}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {5}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.110215.010815a}, url = {http://global-sci.org/intro/article_detail/eajam/10807.html} }
TY - JOUR T1 - Generalised (2+1)-Dimensional Super MKdV Hierarchy for Integrable Systems in Soliton Theory JO - East Asian Journal on Applied Mathematics VL - 3 SP - 256 EP - 272 PY - 2018 DA - 2018/02 SN - 5 DO - http://doi.org/10.4208/eajam.110215.010815a UR - https://global-sci.org/intro/article_detail/eajam/10807.html KW - Soliton theory, generalised Lie superalgebra, (2+1)-dimensional super mKdV hierarchy, supertrace identity, $G′/G^{2}$ method. AB -

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.

Huanhe Dong, Kun Zhao, Hongwei Yang & Yuqing Li. (1970). Generalised (2+1)-Dimensional Super MKdV Hierarchy for Integrable Systems in Soliton Theory. East Asian Journal on Applied Mathematics. 5 (3). 256-272. doi:10.4208/eajam.110215.010815a
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