Journal of Nonlinear Mathematical Physics

Volume 9, Issue Supplement 1, February 2002, Pages 99 - 105

Hamiltonian Structure and Linear Stability of Solitary Waves of the Green-Naghdi Equations

Authors
Yi A. Li
Corresponding Author
Yi A. Li
Received 30 May 2001, Revised 8 July 2001, Accepted 15 July 2001, Available Online 1 February 2002.
DOI
https://doi.org/10.2991/jnmp.2002.9.s1.9How to use a DOI?
Abstract
We investigate linear stability of solitary waves of a Hamiltonian system. Unlike weakly nonlinear water wave models, the physical system considered here is nonlinearly dispersive, and contains nonlinearity in its highest derivative term. This results in more detailed asymptotic analysis of the eigenvalue problem in presence of a large parameter. Combining the technique of singular perturbation with the Evans function, we show that the problem has no eigenvalues of positive real part and solitary waves of small amplitude are linearly stable.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
9 - Supplement 1
Pages
99 - 105
Publication Date
2002/02
ISBN
91-631-2120-4
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.2002.9.s1.9How 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  - Yi A. Li
PY  - 2002
DA  - 2002/02
TI  - Hamiltonian Structure and Linear Stability of Solitary Waves of the Green-Naghdi Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 99
EP  - 105
VL  - 9
IS  - Supplement 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.2002.9.s1.9
DO  - https://doi.org/10.2991/jnmp.2002.9.s1.9
ID  - Li2002
ER  -