| Abstract: | Much attention has been given to constructing Lie and Lie superalgebra forintegrable systems in soliton theory, which often have significant scientific applications.However, this has mostly been confined to (1+1)-dimensional integrable systems, andthere 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 commonLie 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 theHamiltonian structure derives from a generalised supertrace identity. We also obtainsome solutions of the (2+1)-dimensional mKdV equation using the $G′/G^{2}$ method. |
