Interaction of a quasi one-dimensional soliton of the Kadomtsev-Petviashvili (KP-II) equation with a moving local dipole, described by an additional term in the equation, is investigated analytically by means of the Lagrangian-averaging (Whitham's) technique. The main result of the interaction is the generation of leftand right-going flexural waves on the crest of the soliton. The generated fle...

We introduce a dispersionless integrable system which interpolates between the dispersionless Kadomtsev–Petviashvili equation and the hyper–CR equation. The interpolating system arises as a symmetry reduction of the anti–self–dual Einstein equations in (2, 2) signature by a conformal Killing vector whose self–dual derivative is null. It also arises as a special case of the Manakov–Santini integ...

We introduce a dispersionless integrable system which interpolates between the dispersionless Kadomtsev–Petviashvili equation and the hyper–CR equation. The interpolating system arises as a symmetry reduction of the anti–self–dual Einstein equations in (2, 2) signature by a conformal Killing vector whose self–dual derivative is null. It also arises as a special case of the Manakov–Santini integ...

(2 + 1) dimensional Boussinesq and Kadomtsev-Petviashvili equation are investigated by employing Jacobi elliptic function expansion method in this paper. As a result, some new forms traveling wave solutions of the equation are reported. Numerical simulation results are shown. These new solutions may be important for the explanation of some practical physical problems. The results of this paper ...

In this article we study the generalized dispersion version of the Kadomtsev-Petviashvili II equation, on T × R and T × R. We start by proving bilinear Strichartz type estimates, dependent only on the dimension of the domain but not on the dispersion. Their analogues in terms of Bourgain spaces are then used as the main tool for the proof of bilinear estimates of the nonlinear terms of the equa...

We study the maximum wave amplitude produced by line-soliton interactions of the Kadomtsev-Petviashvili II (KPII) equation, and we discuss a mechanism of generation of large amplitude shallow water waves by multi-soliton interactions of KPII. We also describe a method to predict the possible maximum wave amplitude from asymptotic data. Finally, we report on numerical simulations of multi-solito...

This article investigates the local fractional generalized Kadomtsev–Petviashvili equation and Kadomtsev–Petviashvili-modified equal width equation. It presents traveling-wave transformation in a nondifferentiable type for governing equations, which translate them into ordinary differential equations. also solutions certain proposed models, using an ansatz method based on some functions defined...

In this paper, the Kadomtsev-Petviashvili equation is solved by using the Adomian’s decomposition method , modified Adomian’s decomposition method , variational iteration method , modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The existence and uniqueness of the solution and convergence of the proposed...