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

Autor:	Choudhuri, Amitava, Talukdar, B., Das, U.
Rok vydání:	2008
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems
Zdroj:	Z. Naturforsch, 64a, 171-179 (2008)
Druh dokumentu:	Working Paper
DOI:	10.1515/zna-2009-3-403
Popis:	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. Comment: 8 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0801.1763 Zobrazit plný text záznamu View this record from Arxiv