A quantisation of the KP equation on a cylinder is proposed that is equivalent to an infinite system of non-relativistic one-dimensional bosons carrying masses m = 1, 2, . . . The Hamiltonian is Galilei-invariant and includes the split Ψ m1 Ψ m2 Ψm1+m2 and merge Ψ m1+m2 Ψm1Ψm2 terms for all combinations of particles with masses m1, m2 and m1 + m2, with a special choice of coupling constants. Th...

We construct the formal solution of the Cauchy problem for the dispersionless Kadomtsev Petviashvili equation as application of the Inverse Scattering Transform for the vector field corresponding to a Newtonian particle in a time-dependent potential. This is in full analogy with the Cauchy problem for the Kadomtsev Petviashvili equation, associated with the Inverse Scattering Transform of the t...

Note also that when E → ±∞, equation (1.1) transforms into another renowned (2 + 1)dimensional analog of KdV, Kadomtsev-Petviashvili equation (KP-I and KP-II, respectively). In addition, a dispersionless analog of (1.1) at E = 0 was derived in [KM] in the framework of a geometrical optics model. Equation (1.1) is contained implicitly in [M] as an equation possessing the following representation...

We consider a Lie algebra generalizing the Virasoro algebra to the case of two space variables. We study its coadjoint representation and calculate the corresponding Euler equations. In particular, we obtain a bi-Hamiltonian system that leads to an integrable non-linear partial differential equation. This equation is an analogue of the Kadomtsev–Petviashvili (of type B) equation.

Of concern are traveling wave solutions for the fractional Kadomtsev–Petviashvili (fKP) equation. The existence of periodically modulated solitary is proved by dimension-breaking bifurcation. Moreover, line and their transverse (in)stability discussed. Analogous to classical Kadmomtsev–Petviashvili (KP) equation, fKP equation comes in two versions: fKP-I fKP-II. We show that waves transversely ...

governs the dynamics of solitary waves. Firstly, it was derived to describe shallowwater waves of long wavelength and small amplitude. It is a crucial equation in the theory of integrable systems because it has infinite number of conservation laws, gives multiple-soliton solutions, and has many other physical properties. See, for example, [2] and references therein. An essential extension of th...

In this paper, variational iteration method (VIM) is applied to obtain approximate analytical solution of the (2 + 1)-dimensional potential Kadomtsev-Petviashvili equation (PKP) without any discretization. Comparisons with the exact solutions reveal that VIM is very effective and convenient.

By using the complete discrimination system for the polynomial method, the classification of single traveling wave solutions to the generalized Kadomtsev-Petviashvili equation without dissipation terms in is obtained. 2 p 

We find new periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrödinger (NLS) equation, the λφ4 model, the sine-Gordon equation and the Boussinesq equation by making appropriate linear superpositions of known periodic solutions. This unusual procedure for generating solutions of nonlinear differential equations is successful as a consequence of some powerful, recen...