is derived for surface gravity waves with nearly-elliptic front, generalising the cylindrical KP equation for nearly-concentric waves. We discuss transformations between the derived equation and two existing versions of the KP equation, for nearly-plane and nearly-concentric waves. The transformations are used to construct important classes of exact solutions of the derived equation and corresp...

We study a general class of line-soliton solutions of the Kadomtsev-Petviashvili II KPII equation by investigating the Wronskian form of its tau-function. We show that, in addition to the previously known line soliton solutions of KPII, this class also contains a large variety of multisoliton solutions, many of which exhibit nontrivial spatial interaction patterns. We also show that, in general...

The Kadomtsev-Petviashvili reduction method is a crucial to derive the solitonic solutions of (1+1) dimensional integrable system from high system. In this work, we explore use lower construct in one with Darboux transformation. Especially, utilize disclose relationship between rogue wave and lump solutions. Under one-constraint method, asymptotic analysis pattern equation given

Algebro-geometric solutions of the lattice potential modified Kadomtsev-Petviashvili (lpmKP) equation are constructed. A Darboux transformation Kaup--Newell spectral problem is employed to generate a Lax triad for lpmKP equation, as well define commutative integrable symplectic maps which discrete flows eigenfunctions. These share same integrals with finite-dimensional Hamiltonian system associ...

We study soliton solutions of the Kadomtsev-Petviashvili II equation (-4u(t)+6uu(x)+3u(xxx))(x)+u(yy)=0 in terms of the amplitudes and directions of the interacting solitons. In particular, we classify elastic N-soliton solutions, namely, solutions for which the number, directions, and amplitudes of the N asymptotic line solitons as y-->infinity coincide with those of the N asymptotic line soli...

In this paper we obtain existence and (suitable) uniqueness and continuous dependence for the KP-I equation for finite time and small data in the intersection of the energy space and a natural weighted L space.