Higher Order Terms in Multiscale Expansions: A Linearized KdV Hierarchy

DOI

10.2991/jnmp.2002.9.3.6How to use a DOI?

Abstract

We consider a wide class of model equations, able to describe wave propagation in dispersive nonlinear media. The Korteweg-de Vries (KdV) equation is derived in this general frame under some conditions, the physical meanings of which are clarified. It is obtained as usual at leading order in some multiscale expansion. The higher order terms in this expansion are studied making use of a multi-time formalism and imposing the condition that the main term satisfies the whole KdV hierarchy. The evolution of the higher order terms with respect to the higher order time variables can be described through the introduction of a linearized KdV hierarchy. This allows one to give an expression of the higher order time derivatives that appear in the right hand member of the perturbative expansion equations, to show that overall the higher order terms do not produce any secularity and to prove that the formal expansion contains only bounded terms.

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  - Hervé Leblond
PY  - 2002
DA  - 2002/08/01
TI  - Higher Order Terms in Multiscale Expansions: A Linearized KdV Hierarchy
JO  - Journal of Nonlinear Mathematical Physics
SP  - 325
EP  - 346
VL  - 9
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.3.6
DO  - 10.2991/jnmp.2002.9.3.6
ID  - Leblond2002
ER  -