On the existence of solitary waves for Boussinesq type equations and Cauchy problem for a new conservative model. (English) Zbl 1375.35358

Summary: We present a long time existence theory for a new enhanced Boussinesq-Type system with constant bathymetry written in a conservative form. We also prove the existence of solitary wave for a large class of asymptotic models, including Beji-Nadaoka, Madsen-Sorensen and Nwogu equations. Furthermore, we give a procedure to calculate numerically these particular solutions and we present some effective computations.


35Q35 PDEs in connection with fluid mechanics
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35C07 Traveling wave solutions
Full Text: Euclid