Related papers: On nonautonomous differential-difference AKP, BKP …
A unified framework is presented for the solution structure of three-dimensional discrete integrable systems, including the lattice AKP, BKP and CKP equations. This is done through the so-called direct linearising transform which…
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…
The modified Kadomtsev-Petviashvili (mKP) equation is shown in this paper to be decomposable into the first two soliton equations of the 2N-coupled Chen-Lee-Liu and Kaup-Newell hierarchies by respectively nonlinearizing two sets of symmetry…
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…
In this paper we discuss an example of classical integrable equation with rather unusual `B'-type Kadomtsev-Petviashvili (KP) soliton hierarchy.
We represent an algorithm allowing one to construct new classes of partially integrable multidimensional nonlinear partial differential equations (PDEs) starting with the special type of solutions to the (1+1)-dimensional hierarchy of…
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…
We propose a novel semi-discrete Kadomtsev--Petviashvili equation with two discrete and one continuous independent variables, which is integrable in the sense of having the standard and adjoint Lax pairs, from the direct linearisation…
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…
We show that when KP (Kadomtsev-Petviashvili) $\tau$ functions allow special symmetries, the discrete BKP equation can be expressed as a linear combination of the discrete AKP equation and its reflected symmetric forms. Thus the discrete…
Using the generalized symmetry method, we carry out, up to autonomous point transformations, the classification of integrable equations of a subclass of the autonomous five-point differential-difference equations. This subclass includes…
Integrable dispersionless Kadomtsev-Petviashvili (KP) hierarchy of B type is considered. Addition formula for the $\tau$-function and conformally invariant equations for the dispersionless BKP (dBKP) hierarchy are derived. Symmetry…
We introduce a collection of nonlinear integrable partial differential-difference equations that are satisfied by the one-point distribution functions of some classical integrable KPZ models. Moreover, these equations can be regarded as…
We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with…
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, we define the modified formal variable separation approach and show how it determines, in a remarkably simple manner, the decomposition solutions, the B\"acklund transformations, the Lax pair, and the linear superposition…
In the recent paper by Kudryashov [Commun. Nonlinear Sci. Numer. Simulat., 2009, V.14, 3507-3529] seven common errors in finding exact solutions of nonlinear differential equations were listed and discussed in detail. We indicate two more…
Using the generalized symmetry method we finish a classification, started in the article [R.N. Garifullin, R.I. Yamilov and D. Levi, Classification of five-point differential-difference equations, J. Phys. A: Math. Theor. 50 (2017) 125201…
The existence of decomposition solutions of the well-known nonlinear BKP hierarchy is explored. It is shown that these decompositions provide simple and interesting relationships between classical integrable systems and the BKP hierarchy.…
We derive the Kadomtsev-Petviashvili (KP) equation defined over a general associative algebra and construct its N-soliton solution. For the example of the Moyal algebra, we find multi-soliton solutions for arbitrary space-space…