Related papers: Kadomtsev-Petviashvili equation: one-constraint me…
An integrable extension of the Kadomtsev-Petviashvili (KP) and Davey-Stewartson (DS) equations is investigated in this paper.We will refer to this integrable extension as the (4+1)-dimensional Fokas equation. The determinant expressions of…
The Kadomtsev-Petviashvili (KP) equation describes weakly dispersive and small amplitude waves propagating in a quasi-two dimensional situation. Recently a large variety of exact soliton solutions of the KP equation has been found and…
There is considerable fundamental theoretical and applicative interest in obtaining two-dimensional rogue wave similar to one-dimensional rogue wave of the nonlinear Schr\"odinger equation. Here, we first time proposes a self-mapping…
In this paper, Lie symmetry analysis method is applied to the (2+1)-dimensional time fractional Kadomtsev-Petviashvili (KP) equation with the mixed derivative of Riemann-Liouville time-fractional derivative and integer-order $x$-derivative.…
We develop a method based upon the Singular Manifold Method that yields an iterative and analytic procedure to construct solutions for a Bogoyavlenskii-Kadomtsev-Petviashvili equation. This method allows us to construct a rich collection of…
The residual symmetry coming from truncated Painleve expansion of KP equation is nonlocal, which is localized in this paper by introducing multiple new dependent variables. By using the standard Lie group approach, the symmetry reduction…
The celebrated (1+1)-dimensional Korteweg de-Vries (KdV) equation and its (2+1)-dimensional extention, the Kadomtsev-Petviashvili (KP) equation, are two of the most important models in physical science. The KP hierarchy is explicitly…
In this paper, general rogue wave solutions in the massive Thirring (MT) model are derived by using the Kadomtsev-Petviashvili (KP) hierarchy reduction method and these rational solutions are presented explicitly in terms of determinants…
The paper starts from establishing an elliptic direct linearization (DL) scheme for the Kadomtsev-Petviashvili equation. The scheme consists of an integral equation (involving the Lam\'e function) and a formula for elliptic soliton…
By the Sylvester equation $\bL\bM-\bM\bK=\br\bs^{\st}$ together with an evolution equation set of $\br$ and $\bs$, generalized Cauchy matrix approach is established to investigate exact solutions for Kadomtsev-Petviashvili system, including…
We use the singular manifold method to obtain the Lax pair, Darboux transformations and soliton solutions for a (2+1) dimensional integrable equation.
The reduction by restricting the spectral parameters $k$ and $k'$ on a generic algebraic curve of degree $\mathcal{N}$ is performed for the discrete AKP, BKP and CKP equations, respectively. A variety of two-dimensional discrete integrable…
We investigate the generalized (2 + 1) Nizhnik-Novikov-Veselov equation and construct its linear eigenvalue problem in the coordinate space from the results of singularity structure analysis thereby dispelling the notion of weak Lax pair.…
A generalisation of the Lattice Potential Kadomtsev-Petviashvili (LPKP) equation is presented, using the method of Direct Linearisation based on an elliptic Cauchy kernel. This yields a (3+1)-dimensional lattice system with one of the…
In this paper, a variable coefficient Bilinear neural network method is proposed to deal with the analytical solutions of variable coefficient nonlinear partial differential equations. As an example, a Kadomstev-Petviashvili equation with…
The "pseudodual" of Ward's modified chiral model is a dispersionless limit of the matrix Kadomtsev-Petviashvili (KP) equation. This relation allows to carry solution techniques from KP over to the former model. In particular, lump solutions…
This article is a brief review of the results of studying the collapse of sound waves in media with positive dispersion, which is described in terms of the three-dimensional Kadomtsev-Petviashvili (KP) equation. The KP instability of…
We consider a splitting approach for the Kadomtsev--Petviashvili equation with periodic boundary conditions and show that the necessary interpolation procedure can be efficiently implemented. The error made by this numerical scheme is…
The (2+1)-dimensional spherical Kadomtsev-Petviashvili (SKP) equation of J.-K. Xue [Phys. Lett. A 314:479-483 (2003)] fails the Painleve test for integrability at the highest resonance, where a nontrivial compatibility condition for…
There exist two versions of the Kadomtsev-Petviashvili 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…