Exact solutions for \((3+1)\)-dimensional potential-YTSF equation and discrete Kadomtsev-Petviashvili equation. (English) Zbl 1397.35263

Summary: 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.


35Q53 KdV equations (Korteweg-de Vries equations)
39A14 Partial difference equations
35C05 Solutions to PDEs in closed form
35B15 Almost and pseudo-almost periodic solutions to PDEs
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