6 research outputs found
On the Benjamin and related equations
We consider in this paper various theoretical and numerical issues on
classical one dimensional models of internal waves with surface tension.They
concern the Cauchy problem, including the long time dynamic, localized solitons
or multisolitons, the soliton resolution property. We survey known results,
present a few new ones together with open questions and conjectures motivated
by numerical simulations.
A major issue is to emphasize the differences of the qualitative behavior of
solutions with those of the same equations without the capillary term
The existence of weak solutions for a generalized Camassa-Holm equation
A Camassa-Holm type equation containing nonlinear dissipative effect is investigated. A sufficient condition which guarantees the existence of weak solutions of the equation in lower order Sobolev space H(s) with 1 <= s <= 3/2 is established by using the techniques of the pseudoparabolic regularization and some prior estimates derived from the equation itself