Modified KdV hierarchy : Lax pair representation and bi-Hamiltonian structure
Exactly Solvable and Integrable Systems
2015-05-13 v2
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.
Keywords
Cite
@article{arxiv.0801.1763,
title = {Modified KdV hierarchy : Lax pair representation and bi-Hamiltonian structure},
author = {Amitava Choudhuri and B. Talukdar and U. Das},
journal= {arXiv preprint arXiv:0801.1763},
year = {2015}
}
Comments
8 pages, 2 figures