Analytical soliton solutions and wave profiles of the (3+1)-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov equation

Abstract

In this research paper, the improved generalized Riccati equation mapping (IGREM) method is employed to get analytical soliton solutions of (3+1)-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov (mKdV-ZK) equation. By giving appropriate parametric values, we obtain soliton solutions of various types, such as kink soliton, singular soliton, and periodic-singular soliton. The description provided in physical variables allows for the study of genuine multispecies plasmas, plasma models, and frequency regimes. These solutions are essential in illuminating several physical phenomena in engineering and other applied sciences. In addition, 3D and 2D graphs of some selected solutions are sketched for the best physical characterization of the obtained results. This method can also be implemented in many non-linear equations in contemporary research areas. Comparison with previous studies shows that the discovery of singular soliton is novel. Therefore, our research represents a significant advancement in the field and contributes to expanding the knowledge regarding soliton behavior. The applications of this study include electron and ion-acoustic modes in regular plasmas with hot Boltzmann electron species, as well as ion and dust-acoustic modes, depending on the specific modeling of the heavier components.