Global existence of smooth solutions and stability of solitary waves for a generalized Boussinesq equation View Full Text


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Article Info

DATE

1988-03

AUTHORS

Jerry L. Bona, Robert L. Sachs

ABSTRACT

Certain generalizations of one of the classical Boussinesq-type equations, are considered. It is shown that the initial-value problem for this type of equation is always locally well posed. It is also determined that the special, solitary-wave solutions of these equations are nonlinearly stable for a range of their phase speeds. These two facts lead to the conclusion that initial data lying relatively close to a stable solitary wave evolves into a global solution of these equations. This contrasts with the results of blow-up obtained recently by Kalantarov and Ladyzhenskaya for the same type of equation, and casts additional light upon the results for the original version (*) of this class of equations obtained via inverse-scattering theory by Deift, Tomei and Trubowitz. More... »

PAGES

15-29

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01218475

DOI

http://dx.doi.org/10.1007/bf01218475

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1004654010


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