Related papers: Interaction solutions for mKP equation with nonloc…
A nonlocal form of a two-layer fluid system is proposed by a simple symmetry reduction, then by applying multiple scale method to it a general nonlocal two place variable coefficient modified KdV (VCmKdV) equation with shifted space and…
We prove that the non-commutative Kadomtsev-Petviashvili (KP) equation and a `lifted' modified Kadomtsev-Petviashvili (mKP) equation are directly linearisable, and thus integrable in this sense. There are several versions of the…
An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev--Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is given in terms of a…
The soliton resolution for the focusing modified Korteweg-de vries (mKdV) equation is established for initial conditions in some weighted Sobolev spaces. Our approach is based on the nonlinear steepest descent method and its reformulation…
The main purpose of the paper is to provide a survey of our recent studies on soliton solutions of the Kadomtsev-Petviashvili (KP) equation. The classification is based on the far-field patterns of the solutions which consist of a finite…
The Painlev\'e property for a (2+1)-dimensional Korteweg-de Vries (KdV) extension, the combined KP3 (Kadomtsev- Petviashvili) and KP4 (cKP3-4) is proved by using Kruskal's simplification. The truncated Painlev\'e expansion is used to find…
Real and bounded elliptic solutions suitable for applying the Khare-Sukhatme superposition procedure are presented and used to generate superposition solutions of the generalized modified Kadomtsev-Petviashvili equation (gmKPE) and the…
We propose compact finite difference schemes to solve the KP equations $u\_t + u\_{xxx} + u^p u\_x + $\lambda$ \partial^{--1}\_x u\_{yy} = 0$. When $p = 1$, this equation describes the propagation of small amplitude long waves in shallow…
In this paper, the linear spectral problem, which associated with the (n+1)-dimensional generalized Kadomtsev-Petviashvili (gKP) equation, with the Jacobi elliptic function as the external potential is investigated based on the Lam\'{e}…
We consider the scaling similarity solutions of two integrable cubically nonlinear partial differential equations (PDEs) that admit peaked soliton (peakon) solutions, namely the modified Camassa-Holm (mCH) equation and Novikov's equation.…
Gap solitons near a band edge of a spatially periodic nonlinear PDE can be formally approximated by solutions of Coupled Mode Equations (CMEs). Here we study this approximation for the case of the 2D Periodic Nonlinear Schr\"{o}dinger /…
General soliton solutions to a nonlocal nonlinear Schr\"odinger (NLS) equation with PT-symmetry for both zero and nonzero boundary conditions {are considered} via the combination of Hirota's bilinear method and the Kadomtsev-Petviashvili…
In this paper, a complete Lie symmetry analysis of the damped wave equation with time-dependent coefficients is investigated. Then the invariant solutions and the exact solutions generated from the symmetries are presented. Moreover, a Lie…
A numerical study of the nonlinear wave solutions of the Rosenau-Pikovsky K(cos) equation is presented. This equation supports at least two kind of solitary waves with compact support: compactons of varying amplitude and speed, both…
In this paper, we investigate the non-autonomous discrete Kadomtsev-Petviashvili (KP) system in terms of generalized Cauchy matrix approach. These equations include non-autonomous bilinear lattice KP equation, non-autonomous lattice…
Full dispersive models of water waves, such as the Whitham equation and the full dispersion Kadomtsev-Petviashvili (KP) equation, are interesting from both the physical and mathematical points of view. This paper studies analogous full…
By considering the inhomogeneities of media, a generalized variable-coefficient Kadomtsev-Petviashvili (vc-KP) equation is investigated, which can be used to describe many nonlinear phenomena in fluid dynamics and plasma physics. In this…
We study the nonlocal modified Korteweg-de Vries (mKdV) equations obtained from AKNS scheme by Ablowitz-Musslimani type nonlocal reductions. We first find soliton solutions of the coupled mKdV system by using the Hirota direct method. Then…
We consider a space-inhomogeneous Kolmogorov-Petrovskii-Piskunov (KPP) equation with a nonlocal diffusion and an almost-periodic nonlinearity. By employing and adapting the theory of homogenization, we show that solutions of this equation…
A new three-dimensional second-order nonlinear wave equation is introduced which passes the Painleve test for integrability and possesses KdV-type multisoliton solutions. Lax integrability of this equation remains unknown.