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arXiv · 0801.1763

Modified KdV hierarchy : Lax pair representation and bi-Hamiltonian structure

Amitava Choudhuri·B. Talukdar·U. Das
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Abstract

We consider equations in the modified KdV (mKdV) hierarchy and make use of the Miura transformation to construct expressions for their Lax pair. We derive a Lagrangian-based approach to study the bi-Hamiltonian structure of the mKdV equations. We also show that the complex modified KdV (cmKdV) equation follows from the action principle to have a Lagrangian representation. This representation not only provides a basis to write the cmKdV equation in the canonical form endowed with an appropriate Poisson structure but also help us construct a semianalytical solution of it. The solution obtained by us may serve as a useful guide for purely numerical routines which are currently being used to solve the cmKdV eqution.

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Amitava Choudhuri, B. Talukdar, U. Das. 2008-01-11. Modified KdV hierarchy : Lax pair representation and bi-Hamiltonian structure. https://doi.org/10.1515/zna-2009-3-403

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