A Nonlinearly Dispersive Fifth Order Integrable Equation and its Hierarchy

DOI

10.2991/jnmp.2005.12.1.9How to use a DOI?

Abstract

In this paper, we study the properties of a nonlinearly dispersive integrable system of fifth order and its associated hierarchy. We describe a Lax representation for such a system which leads to two infinite series of conserved charges and two hierarchies of equations that share the same conserved charges. We construct two compatible Hamiltonian structures as well as their Casimir functionals. One of the structures has a single Casimir functional while the other has two. This allows us to extend the flows into negative order and clarifies the meaning of two different hierarchies of positive flows. We study the behavior of these systems under a hodograph transformation and show that they are related to the Kaup-Kupershmidt and the Sawada-Kotera equations under appropriate Miura transformations. We also discuss briefly some properties associated with the generalization of second, third and fourth order Lax operators.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Ashok Das
AU  - Ziemowit Popowicz
PY  - 2005
DA  - 2005/02/01
TI  - A Nonlinearly Dispersive Fifth Order Integrable Equation and its Hierarchy
JO  - Journal of Nonlinear Mathematical Physics
SP  - 105
EP  - 117
VL  - 12
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2005.12.1.9
DO  - 10.2991/jnmp.2005.12.1.9
ID  - Das2005
ER  -