Journal of Nonlinear Mathematical Physics

Volume 9, Issue 3, April 2001, Pages 325 - 346

Higher Order Terms in Multiscale Expansions: A Linearized KdV Hierarchy

Authors
Hervé LEBLOND
Corresponding Author
Hervé LEBLOND
Available Online 11 December 2006.
DOI
https://doi.org/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.
Open Access
This is an open access article distributed under the CC BY-NC license.

Download article (PDF)

Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - 3
Pages
325 - 346
Publication Date
2006/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2002.9.3.6How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Hervé LEBLOND
PY  - 2006
DA  - 2006/12
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  - https://doi.org/10.2991/jnmp.2002.9.3.6
ID  - LEBLOND2006
ER  -