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1 results

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

  • Huanhe Dong, Kun Zhao, Hongwei Yang, Yuqing Li
  • Journal:
    East Asian Journal on Applied Mathematics / Volume 5 / Issue 3 / August 2015
    Published online by Cambridge University Press:
    07 September 2015, pp. 256-272
    Print publication:
    August 2015

  • 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.