Combined Exp-function ansatz method and applications. (English) Zbl 1304.35178

Mu, Gui; Liu, Jun; Dai, Zhengde

Univers. J. Math. Math. Sci. 1, No. 2, 189-196 (2012).

Summary: We propose a combined Exp-function ansatz method, which is a direct method based on Hirota bilinear form to obtain novel exact solutions of nonlinear partial differential equation. Taking the Calogero equation as an example, many new type analytical solutions are obtained, and these solutions exhibit interesting dynamic diversity graphically.

MSC:

35C05	Solutions to PDEs in closed form
35Q51	Soliton equations
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35G20	Nonlinear higher-order PDEs

Keywords:

Calogero equation; Hirota’s bilinear method