ISSN:
1432-1467
Keywords:
nearly integrable systems
;
spectral transform
;
attractors
;
traveling waves
;
stability
;
numerical methods
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Summary In this paper we rigorously show the existence and smoothness inε of traveling wave solutions to a periodic Korteweg-deVries equation with a Kuramoto-Sivashinsky-type perturbation for sufficiently small values of the perturbation parameterε. The shape and the spectral transforms of these traveling waves are calculated perturbatively to first order. A linear stability theory using squared eigenfunction bases related to the spectral theory of the KdV equation is proposed and carried out numerically. Finally, the inverse spectral transform is used to study the transient and asymptotic stages of the dynamics of the solutions.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02429875
Permalink
