Non-singular complexiton, singular complexiton and complex N-soliton solutions of the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Abstract

The central target of this work is to extract some novel exact solutions of the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation (BLMPE) for the incompressible fluid. By applying the weight algorithm (WA) and linear superposition principle (LSP), we construct two sets of the complexiton solutions, which are the non-singular complexiton and singular complexiton solution via introducing the pairs of the conjugate parameters. In addition, we also explore the complex N-soliton solutions (CNSSs) via the Hirota bilinear equation (HBE) that is developed by the Cole-Hopf transform (CHT). The outlines of the corresponding exact solutions are presented graphically. As far as the information currently available, the derived solutions in this exploration are all new and are expected to enable us to investigate the dynamic characteristics of the considered equation better.

Multi-lump, resonant Y-shape soliton, complex multi kink solitons and the solitary wave solutions to the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation for incompressible fluid

“…Then we get the complex two kink solitons solution as: We can set the complex three kink solitons solution as [48,49]: where…”

Diverse soliton solutions to the nonlinear partial differential equations related to electrical transmission line

“…Recent studies have made significant contributions, illuminating the applicability of the Hirota bilinear method. For instance, the examination of complex N-soliton solutions and soliton molecules in the new extended (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation highlights the method's utility [31]. In addition, the investigation of novel complex multiple kink soliton solutions for the generalized (3+1)dimensional Kadomtsev-Petviashvili equation has shown the method's effectiveness in revealing complex nonlinear dynamics [32].…”