ISSN:
1432-1467
Keywords:
solitary waves
;
stability
;
nonlinear dispersive wave equations
;
model equations for long waves
;
Korteweg-de Vries-type equations
;
regularized long-wave equations
;
nonlinear Schrödinger equations
;
35B35
;
35B40
;
35Q35
;
35Q51
;
35Q53
;
35Q55
;
35S10
;
76B15
;
76B25
;
76E30
;
86A05
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Summary After a review of the existing state of affairs, an improvement is made in the stability theory for solitary-wave solutions of evolution equations of Korteweg-de Vries-type modelling the propagation of small-amplitude long waves. It is shown that the bulk of the solution emerging from initial data that is a small perturbation of an exact solitary wave travels at a speed close to that of the unperturbed solitary wave. This not unexpected result lends credibility to the presumption that the solution emanating from a perturbed solitary wave consists mainly of a nearby solitary wave. The result makes use of the existing stability theory together with certain small refinements, coupled with a new expression for the speed of propagation of the disturbance. The idea behind our result is also shown to be effective in the context of one-dimensional regularized long-wave equations and multidimensional nonlinear Schrödinger equations.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02430641
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