Exact solutions of nonlinear equations in mathematical physics via negative power expansion method. (English) Zbl 1490.35378
Summary: In this paper, a direct method called negative power expansion (NPE) method is presented and extended to construct exact solutions of nonlinear mathematical physical equations. The presented NPE method is also effective for the coupled, variable-coefficient and some other special types of equations. To illustrate the effectiveness, the \((2 + 1)\)-dimensional dispersive long wave (DLW) equations, Maccari’s equations, Tzitzeica-Dodd-Bullough (TDB) equation, Sawada-Kotera (SK) equation with variable coefficients and two lattice equations are considered. As a result, some exact solutions are obtained including traveling wave solutions, non-traveling wave solutions and semi-discrete solutions. This paper shows that the NPE method is a simple and effective method for solving nonlinear equations in mathematical physics.
MSC:
| 35Q51 | Soliton equations |
| 35J99 | Elliptic equations and elliptic systems |
| 68W30 | Symbolic computation and algebraic computation |
Keywords:
exact solution; NPE method; \((2+1)\)-dimensional DLW equations; Maccari’s equations; TDB equation; SK equation with variable coefficients; lattice equationsReferences:
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