Abstract
By combining the extended homoclinic test approach (EHTA) with the method of separation of variables explicit exact non-traveling wave solutions of the (3+1)-dimensional potential Yu-Toda-Sasa-Fukuyama (YTSF) equation is constructed. With the aid of symbolic computation, abundant new explicit exact solutions of the (3+1)-dimensional potential-YTSF equation are obtained. The results obtained her e reveal the complex structure of the solutions of the (3+1) dimensional potential-YTSF equation. Many of the previous results obtained in other literature can be seen as special cases here. When some arbitrary functions included in these solutions are taken as some special functions, exact periodic solitary wave, periodic soliton, periodic cross-kink wave, periodic two-solitary wave are presented.
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