We first review the known mathematical results concerning the Kadomtsev–Petviashvili type
equations. Then we perform numerical simulations to analyze various qualitative properties …

We present a general result of transverse nonlinear instability of 1d solitary waves for
Hamiltonian PDE's for both periodic or localized transverse perturbations. Our main …

In this paper, the finite difference method is employed to solve Kadomtsev–Petviashvili–
Benjamin–Bona–Mahony II (KP–BBM-II) partial differential equations. The time and space …

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This paper deals with the propagation of the one-directional small amplitude long waves in
shallow water. In the conservative context, such waves are described by the Korteweg-de …

Le but de cette thèse est d'étudier certaines équations aux dérivées partielles hyperboliques-
dispersives. Une part importante est consacrée à l'analyse numérique et plus …

We propose compact finite difference schemes to solve the KP equations $ u\_t+ u\_ {xxx}+
u^ pu\_x+ $\lambda $\partial^{--1}\_x u\_ {yy}= 0$. When $ p= 1$, this equation describes the …

We study the unique continuation property for the generalized Kadomtsev–Petviashvili (KP)
equations and its regularized version. We use Carleman estimates to prove that if the …

The aim of this thesis is to study some hyperbolic-dispersive partial differential equations. A
significant part is devoted to the numerical analysis and more precisely to the convergence …