Dynamics of the soliton waves, breather waves, and rogue waves to the cylindrical Kadomtsev-Petviashvili equation in pair-ion–electron plasma

Abstract

A lot of work has been reported to present some numerical results on pair-ion–electron plasmas. However, very few works have reported the corresponding mathematical analytical results in these aspects. In this work, we study a cylindrical Kadomtsev-Petviashvili (CKP) equation, which can be derived from pair-ion–electron plasmas. We further report some interesting mathematical analytical results, including some dynamics of soliton waves, breather waves, and rogue waves in pair-ion–electron plasma via the CKP equation. Using a novel gauge transformation, the Grammian N-soliton solutions of the CKP equation are found analytically. Based on the bilinear transformation method, the breather wave solutions are obtained explicitly under some parameter constraints. Furthermore, we construct the rogue waves using the long wave limit method. In addition, some remarkable characteristics of these soliton solutions are analyzed graphically. According to analytic solutions, the influences of each parameter on the dynamics of the soliton waves, breather waves, and rogue waves are discussed, and the method of how to control such nonlinear phenomena is suggested.