Physics

Nonlinear system

Homoclinic orbit

Bilinear interpolation

Bifurcation

Mathematics

Partial differential equation

Statistics

Connection (principal bundle)

Symbolic computation

Mathematical analysis

One-dimensional space

Kadomtsev–Petviashvili equation

Geometry

Characteristic equation

Quantum mechanics

Breather

Soliton

Bilinear form

International Journal of Numerical Methods for Heat &amp Fluid Flow

Purpose The purpose of this paper is to explore new reduced form of the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili (BKP) equation by considering its bilinear equations, derived from connection between the Hirota’s transformation and Bell polynomials. Design/methodology/approach Based on the bilinear form of new reduced form of the (3 + 1)-dimensional generalized BKP equation, lump solutions with sufficient and necessary conditions to guarantee analyticity and rational localization of the solutions are discovered. Also, extended homoclinic approach is applied to considered equation for finding solitary wave solutions. Findings A class of the bright-dark lump waves are fabricated for studying different attributes of (3 + 1)-dimensional generalized BKP equation and some new exact solutions including kinky periodic solitary wave solutions and line breathers periodic are also obtained by Following the extended homoclinic approach. Research limitations/implications The paper presents that the implemented methods have emerged as a promising and robust mathematical tool to manage (3 + 1)-dimensional generalized BKP equation by using the Hirota’s bilinear equation. Practical implications By considering important characteristics of lump and solitary wave solutions, one can understand the shapes, amplitudes and velocities of solitons after the collision with another soliton. Social implications The analysis of these higher-dimensional nonlinear wave equations is not only of fundamental interest but also has important practical implications in many areas of mathematical physics and ocean engineering. Originality/value To the best of the authors’ knowledge, the acquired solutions given in various cases have not been reported for new reduced form of the (3 + 1)-dimensional generalized BKP equation in the literature. These obtained solutions are advantageous for researchers to know objective laws and grab the indispensable features of the development of the mathematical physics.

Lump, breather and solitary wave solutions to new reduced form of the generalized BKP equation