Volume 12, Issue 1, February 2005, Pages 105 - 117
A Nonlinearly Dispersive Fifth Order Integrable Equation and its Hierarchy
Ashok Das, Ziemowit Popowicz
Received 29 June 2004, Accepted 4 October 2004, Available Online 1 February 2005.
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- 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.
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Cite this article
TY - JOUR AU - Ashok Das AU - Ziemowit Popowicz PY - 2005 DA - 2005/02 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 - https://doi.org/10.2991/jnmp.2005.12.1.9 ID - Das2005 ER -