Propagation of collisional among multi-soliton, multi-singular solition and rogue wave around the critical values in an unmagetized plasma

Abstract

Progress in understanding the propagation characteristics of (i) collisional acoustic among multi-soliton and multi-singular soliton around the critical values and their corresponding phase shifts and (ii) collision between two rogue waves (RWs) propagating toward each in a plasma environment is presented. The considered plasma environment consists of mobile cold positrons, immobile positive ions and (r, q)-distributed hot positrons, and electrons. To accomplish our goal, the coupled modified Korteweg–de Vries equations (mKdVEs) and nonlinear Schrödinger equations (NLSEs) are derived from the considered plasma environment. Based on the concept of Hirota's bilinear method, the multi-soliton and multi-singular soliton solutions of the coupled mKdVEs are determined directly. In addition, the analytical unstable RWs solutions of the coupled NLSEs are determined. With the impact of physical parameters, (i) the trajectories are described for double, triple, quadruple and quintuple positron acoustic bi-directional multi-soliton and (ii) the variation of collisional RWs profiles are displayed with physical interpretation. The results described by the coupled mKdVEs also show that the scattered double-, triple-, quadruple-, and quintuple-soliton are elastic and preserved their original features oppositely after the collision around the critical value of any specific plasma parameter.