Related papers: Kadomtsev-Petviashvili equation: one-constraint me…
This paper discusses the construction of a new $(3+1)$-dimensional Korteweg-de Vries (KdV) equation. By employing the KdV's recursion operator, we extract two equations, and with elemental computation steps, the obtained result is $…
In this paper we use variational methods to establish a Berestycki-Lions type result for a class of generalized Kadomtsev-Petviashvili equation in $\mathbb{R}^N$. The positive and zero mass cases are considered.
In the paper we investigate integrability characteristics for the dispersionless Kadomtsev-Petviashvili hierarchy. These characteristics include symmetries, Hamiltonian structures and conserved quantities. We give a Lax triad to construct a…
The nonlocal symmetries for the modified Kadomtsev-Petviashvili (mKP) equation are obtained with the truncated Painleve method. The nonlocal symmetries can be localized to the Lie point symmetries by introducing auxiliary dependent…
We study conditions of reduction of the multidimensional wave equation - a system of the d'Alembert and Hamilton equations. We prove necessary conditions for compatibility of such system of the reduction conditions. Possible types of the…
In this paper, we study the existence and concentration of solitary waves for a class of generalized Kadomtsev-Petviashvili equations with the potential in $\mathbb{R}^2$ via the variational methods.
The Relativistic one dimensional Coulomb problem was studied by means of the Path Integral Monte Carlo method. Relativistic and non-relativistic regimes of this problem were investigated. The relativistic regime appears at small masses of…
A complete classification of compacton solutions is carried out for a generalization of the Kadomtsev-Petviashvili (KP) equation involving nonlinear dispersion in two and higher spatial dimensions. In particular, precise conditions are…
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…
Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our…
We consider the Kadomtsev-Petviashvili (KP) equations posed on $\mathbb{R}^2$. For both equations, we provide sequential in time asymptotic descriptions of solutions, of arbitrarily large data, inside regions not containing lumps or line…
The logarithmic derivative of the marginal distributions of randomly fluctuating interfaces in one dimension on a large scale evolve according to the Kadomtsev-Petviashvili (KP) equation. This is derived algebraically from a Fredholm…
With the assistance of one fold Darboux transformation formula, we derive rogue wave solutions of the complex modified Korteweg-de Vries equation on an elliptic function background. We employ an algebraic method to find the necessary…
Dispersive shock waves (DSWs) in the Kadomtsev-Petviashvili (KP) equation and two dimensional Benjamin-Ono (2DBO) equation are considered using parabolic front initial data. Employing a front tracking type ansatz exactly reduces the study…
We investigate the asymptotic behaviour of the localised solitary waves for the generalised Kadomtsev-Petviashvili equations. In particular, we compute their first order asymptotics in any dimension $N \geq 2$.
We extend the key idea behind the generalized Petviashvili method of Ref. \cite{gP} by proposing a novel technique based on a similar idea. This technique systematically eliminates from the iteratively obtained solution a mode that is…
In this work, we propose a new approach called ``stationary reduction method based on nonisospectral deformation of orthogonal polynomials" for deriving discrete Painlev\'{e}-type (d-P-type) equations. We apply this approach to…
We extend Gesztesy-Holden's method to 2+1 dimensional case to obtain a unified construction to the algebro-geometric solutions of the whole modified Kadomtsev-Petviashvili (mKP) hierarchy. Our tools include the relations between solutions…
We demonstrate that an important class of nonlinear stationary solutions of the three-dimensional (3D) Gross-Pitaevskii equation (GPE) exhibiting nontrivial transversal configurations can be found and characterized in terms of an effective…
This paper develops a hybridizable discontinuous Galerkin method for the two-dimensional Camassa--Holm--Kadomtsev--Petviashvili equation. The method employs Cartesian meshes with tensor-product polynomial spaces, enabling separate treatment…