An investigation on explicit exact non-traveling wave solutions of the (3+1)-dimensional potential Yu–Toda–Sasa–Fukuyama equation

Abstract

Abstract This paper is devoted to investigating new non-traveling wave solutions for the (3 + 1)-dimensional potential Yu–Toda–Sasa–Fukuyama (YTSF) equation. By using the generalized variable separation method and extended three-wave approach, the process of solving the (3 + 1)-dimensional potential-YTSF equation is simplified and the interactions of multiple waves are revealed. With the aid of Maple, we derive thirty-six types new exact explicit non-traveling wave solutions with a like-parabolic tail. The main characteristic of these solutions is that they contain three arbitrary functions, which greatly enrich the diversity of solutions. This characteristic shows the novelty of our work. In particular, selecting suitable arbitrary functions, we can obtain traveling solutions, such as kink-wave solutions, solitary-wave solutions, kinky breather-wave solutions, singular solutions and periodic solutions. Then, some dynamical phenomena are exhibited by 3D representation, providing the complicated structure of the non-traveling wave solutions for the (3 + 1) dimensional potential-YTSF equation and their physical interpretation. In addition, our findings improve and extend the existing literature on related topics.