Analysis of dynamics of fusion solitons of the generalized (3 +1)−Kadomtsev–Petviashvili equation

Abstract

The aim of this paper is to introduce a generalized $(3+1)$-Kadomtsev-Petviashvili equation which is used to describe waves in a ferromagnetic medium. The equation's bilinear form is created and the new homoclinic test approach based on the Hirota bilinear form is used to find numerous novel precise solutions. These accurate solutions, which are depicted in the contour, two-dimensional and three-dimensional graphs, show the evolution of periodic characteristics. The modulation instability is used to investigate the stability of the obtained solutions. Additionally, the development of the fusion soliton is examined, as well as the fusion phenomenon in the traveling wave solution is described in the physical discussion. For this evolution equation, the study indicates new mechanical structures and various characteristics. The derived results back up the model that was proposed. These discoveries open up a new avenue for us to investigate the concept further.

Keywords

• the new homoclinic test approach
• stability analysis
• fusion soliton
• kink soliton
• hirota bilinear method