Exact Solutions for (3+1)-Dimensional Potential-YTSF Equation and Discrete Kadomtsev-Petviashvili Equation

Abstract

By employing Hirota bilinear method, we mainly discuss the ($3+1$)-dimensional potential-YTSF equation and discrete KP equation. For the former, we use the linear superposition principle to get its $N$ exponential wave solutions. In virtue of some Riemann theta function formulas, we also construct its quasiperiodic solutions and analyze the asymptotic properties of these solutions. For the latter, by using certain variable transformations and identities of the theta functions, we explicitly investigate its periodic waves solutions in terms of one-theta function and two-theta functions.