Applications of the combined tanh function method with symmetry method to the nonlinear evolution equations. (English) Zbl 1114.65356

Zhi, Hongyan; Zhang, Hongqing

Appl. Math. Comput. 188, No. 1, 385-393 (2007).

Summary: Based on the symbolic computation, we combine the tanh function method with the symmetry method to construct new type of solutions of the nonlinear evolution equations for the first time. With the combined method, some new types of solutions of the coupled \((2 + 1)\)-dimensional nonlinear system of Schrödinger equations are obtained and their properties are studied by analyzing their figures.

MSC:

65M70	Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q55	NLS equations (nonlinear Schrödinger equations)
68W30	Symbolic computation and algebraic computation

Keywords:

symmetry method; tanh function method; Schrödinger equations; exact solution; symbolic computation; nonlinear evolution equation

Software:

MACSYMA

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