There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispe...

We investigate the properties of finite energy travelling waves to the nonlinear Schrödinger equation with nonzero conditions at infinity for a wide class of nonlinearities. In space dimension two and three we prove that travelling waves converge in the transonic limit (up to rescaling) to ground states of the Kadomtsev-Petviashvili equation. Our results generalize an earlier result of F. Béthu...

Blow up and instability of solitary wave solutions to a generalized Kadomtsev– Petviashvili equation and two-dimensional Benjamin–Ono equations BY JIANQING CHEN*, BOLING GUO AND YONGQIAN HAN School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, People’s Republic of China Institute of Applied Physics and Computational Mathematics, PO Box 8009, Beijing 100088, Peopl...

The solitary wave solution of the quadratic nonlinear Schrd̈inger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution. Keywords—soliton, iterative method, spectral method, plasma

In this paper we establish the local and global well-posedness of the real valued fifth order Kadomstev-Petviashvili I equation in the anisotropic Sobolev spaces with nonnegative indices. In particular, our local well-posedness improves SautTzvetkov’s one and our global well-posedness gives an affirmative answer to SautTzvetkov’s L-data conjecture.

We generalize a method introduced by Bourgain in [2] based on complex analysis to address two spatial dimensional models and prove that if a sufficiently smooth solution to the initial value problem associated with the Kadomtsev-Petviashvili (KP-II) equation (ut + uxxx + uux)x + uyy = 0, (x, y) ∈ R, t ∈ R, is supported compactly in a nontrivial time interval then it vanishes identically.

We study transverse stability and instability of one-dimensional small-amplitude periodic travelling waves a generalized Kadomtsev–Petviashvili equation with respect to two-dimensional perturbations, which are either or square-integrable in the direction propagation underlying wave direction. obtain results KP-fKdV, KP-ILW KP-Whitham equations. Moreover, assuming spectral we aforementioned