Study of N=1 and N=2 supersymmetric integrable hierarchies and their soliton solutions

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Integrable models have seen major advances in the last four decades bringing together various branches of mathematics and having diverse physical applications. Of great interest is the realization that integrable systems give rise to nondispersive, localized travelling wave solutions called solitons. The task of constructing such solutions have resulted in the development of many different techniques to solve these systems, which are non-linear, partial differential equations and difficult to solve analytically. Another characteristic of integrable models is that they are Hamiltonian systems and their Hamiltonian structures are closely related to the conformal algebras. This was made clear when it was shown that the second Hamiltonian structure of the KdV hierarchy is isomorphic to non-linear algebras known as the Wn algebras. Later on the symmetry structures associated with the KP hierarchy, which includes the KdV hierarchy have been investigated
Supervisor:Sasanka Ghosh