Multiple lump molecules and interaction solutions of the Kadomtsev–Petviashvili I equation

Abstract

In this paper, a modified version of the solution in form of Grammian formula is employed to investigate a new type of multiple lump molecule solution of the Kadomtsev-Petviashvili I equation. The high-order multiple lump molecules consisting of M N-lump molecules are constructed by means of the Mth-order determinant and the non-homogeneous polynomial in the degree of 2N. The interaction solutions describing P line solitons radiating P of the M N-lump molecules are constructed. The dynamic behaviors of some specific solutions are analyzed through numerical simulation. All the results will enrich our understanding about the multiple lump waves of the Kadomtsev-Petviashvili I equation.

Highly Dispersive Optical Solitons with Quadratic-Cubic Nonlinear form of Self-Phase Modulation by Sardar Sub-Equation Approach

“…In this approach, we solve Eq. ( 16) by assuming that the solution conforms to the form described in [15][16][17][18][19][20][21]:…”

Novel soliton molecule solutions for the second extend (3+1)-dimensional Jimbo-Miwa equation in fluid mechanics

“…Based the bilinear form, like the lump molecule solution which does not exist in many (2+1)-dimensional integrable models, such as the (2+1)-dimensional generalized Bogoyavlensky-Konopelchenko model [38], Kadomtsev-Petviashvili (KP) system [39], (3+1)-dimensional nagative order KdV-CBS model [47], etc. But for KP systerm, lump molecules can be discovered by using the reduced version of the Grammian form [35,40]. With the aid of equation (17), we find the lump molecule solution in equation (2), which needs to cater for ( ) , the distance between the centres of two single lump solution is constant.…”

Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

“…The lump wave is a remarkable localized wave solution degenerating in the whole space. [1][2][3][4][5][6][7] The lump solution is actually a kind of rational solutions from a mathematical point of view, whose simplest form was first discovered by means of the dressing method and the Hirota's bilinear method. [8][9][10] This solution consists of multiple localized peaks remaining their velocities and trajectories unchanged before and after the interactions.…”