Abstract : In this paper, 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.
Stevan Bellec, Mathieu Colin. On the existence of solitary waves for Boussinesq type equations and a new conservative model.. Advances in Differential Equations, Khayyam Publishing, 2016, 21 (9,10), pp.945-976. ⟨hal-01378585⟩