Bilinear Bäcklund transformation, soliton and breather solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics

Abstract

A (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynam-ics and plasma physics is hereby investigated. Via the Hirota method, bilinear Bäcklund transformation are obtained, along with two types of the analytic solutions. Kink-shaped soliton solutions are derived via the Hirota method. Breather solutions are derived via the extended homoclinic test approach and lump solutions are obtained from the breather solutions under a limiting procedure. We find that the shape and amplitude of the one-kink soliton keep unchanged during the propagation and the velocity of the one-kink soliton depends on all the coefficients in the equation. We graphically demonstrate that the interaction between the two-kink solitons is elastic, and analyse the solitons with the influence of the coefficients. We observe that the amplitudes and shapes of the breather and lump remain unchanged during the propagation, and graphically present the breathers and lumps with the influence of the coefficients in the equation.

Localized nonlinear waves on spatio-temporally controllable backgrounds for a (3+1)-dimensional Kadomtsev-Petviashvili-Boussinesq model in water waves

“…Among these techniques, the Bäcklund transformations is one of the very successful approach to obtain localized wave solutions due to its ease and wide applicability. This approach is being successfully applied to several nonlinear models including single-component (scalar) and vector/coupled (multi-component) systems in one-dimension ((1+1)D) as well as in higher-dimensional ((2+1)D and (3+1)D) equations with different types of nonlinearities [15][16][17][18][19][20][21], to mention a few. Especially, the nature of solitons, breathers, lump and rogue waves in higher-order (1+1)D Boussinesq-Burgers equation [15], (2+1)D dispersive long-wave system [16], (2+1)D coupled Burgers model [17], (3+1)D variable-coefficient Kadomtsev-Petviashvili-Burgers-type equation [18], (3+1)D shallow-water waves [19], (3+1)D generalized Kadomtsev-Petviashvili equation [20] and inhomogeneous coupled nonlinear Schrödinger system [21] are studied using Bäcklund transformation method.…”

Residual symmetries, consistent-Riccati-expansion integrability, and interaction solutions of a new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation

“…As is known, nonlinear integrable evolution equations have been used in many nonlinear fields, such as fluid mechanics, [1][2][3] nonlinear optics, [4][5][6] plasma physics, [7,8] ferrimagnetics [9] and Bose-Einstein condensation. [10] A class of physically important integrable equations, such as the KP equation and the cubic gKP equation, has been applied to describe long wave propagation of small amplitude propagating in plasma physics [11,12] and the collapse of ultrashort spatiotemporal pulses in nonlinear optics.…”