Electron acoustic counterpropagating multi-solitons and rogue waves collision in an unmagnetized plasma in the presence of critical density ratios

In this paper, the nonlinear propagation of electrostatic collisional among multi-solitons around the critical values along with their corresponding phase shifts and collision between two rouge waves propagating toward each other is studied in an unmagnetized plasma environment. Using the concept of Hirota’s bilinear method, the useful forms of multi-solitons solutions of the coupled modified Korteweg–de Vries equations (mKdVEs) are determined. Furthermore, the coupled nonlinear Schrödinger equations (NLSEs) are derived from mKdVEs using the appropriate starching coordinates. The analytic solutions of different orders for the coupled NLSEs are also presented. The effects of the parameters related to the plasma environment on the electron acoustic scattered solitons, phase shifts and scattered rouge waves are analyzed. The proposed results provide the theoretical guidance to understand the propagation characteristics of collisional solitons, and their phase shifts around the critical values and collisional rouge waves in the modulated ranges.