Ontology type: schema:ScholarlyArticle
1988-03
AUTHORSJerry L. Bona, Robert L. Sachs
ABSTRACTCertain 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... »
PAGES15-29
http://scigraph.springernature.com/pub.10.1007/bf01218475
DOIhttp://dx.doi.org/10.1007/bf01218475
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