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 - <p style="text-align: justify;">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.</p>