An improved generalized \(F\)-expansion method and its application to the \((2 + 1)\)-dimensional KdV equations. (English) Zbl 1221.35384
Summary: An improved generalized \(F\)-expansion method is proposed to seek exact solutions of nonlinear partial differential equations. With the aid of symbolic computation, we choose the \((2 + 1)\)-dimensional KdV equations to illustrate the validity and advantages of the proposed method. Many new and more general non-travelling wave solutions are obtained, including single and combined non-degenerate Jacobi elliptic function solutions, soliton-like solutions, trigonometric function solutions, each of which contains two arbitrary functions.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 33E05 | Elliptic functions and integrals |
| 35-04 | Software, source code, etc. for problems pertaining to partial differential equations |
| 35C05 | Solutions to PDEs in closed form |
| 35Q51 | Soliton equations |
Keywords:
\(F\)-expansion method; Jacobi elliptic function; soliton-like solution; trigonometric function solutionReferences:
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