Complexiton, complex multiple kink soliton and the rational wave solutions to the generalized (3 + 1)-dimensional kadomtsev-petviashvili equation

Abstract

Some new exact solutions of the generalized (3+1)-dimensional Kadomtsev-Petviashvili equation (KPE) are explored in this study. Firstly, the resonant multiple soltion solutions (RMSs) are discussed via employing the linear superposition principle and weight algorithm. Then, by introducing pairs of the conjugate parameters to the RMSs, the complexiton solutions including the non-singular complexiton and singular complexiton solutions are extracted. In addition, the complex multiple kink soliton solutions are also probed by employing the bilinear approach. Finally, we investigate the rational wave solutions via the test function method and symbolic computation. By choosing the appropriate parameters, the graph descriptions of the derived solutions are presented to show the dynamical properties. The outcomes of this work are desirous to bring some new perspective to the study of the complexiton, complex solutions and rational wave solutions to the other PDEs.

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…”

Exploring the chaotic structure and soliton solutions for (3 + 1)-dimensional generalized Kadomtsev–Petviashvili model

“…In 13 , the author analyzed the Hirota N-soliton conditions of three (2+1)-dimensional integrable equations. Wang and Li 14 employed a bilinear technique to find novel exact solutions for the generalized (3+ 1)-dimensional Kadomtsev-Petviashvili problem. The NLEEs and their integrability have been studied using a wide range of effective techniques including, Inverse scattering technique 15 , Painlev analysis 16 , Generalized symmetry technique 17 , the extended sinh-Gordon equation expansion method 18 , Bäcklund transformation technique 19 , Pfaffian technique 20 , Hirota bilinear technique 21 , and many others 22 – 25 .…”

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

“…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].…”