Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation. (English) Zbl 1092.37054

Wang, Mingliang; Li, Xiangzheng

Chaos Solitons Fractals 24, No. 5, 1257-1268 (2005).

Summary: We present an extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the new Hamiltonian amplitude equation. When the modulus \(m\) approaches to 1 and 0, then the hyperbolic function solutions (including the solitary wave solutions) and trigonometric function solutions are also given, respectively. As the parameter \(e\) goes to zero, the new Hamiltonian amplitude equation becomes the well-known nonlinear Schrödinger equation (NLS), and at least, 37 kinds of solutions of NLS can be derived from the solutions of the new Hamiltonian amplitude equation.

MSC:

37N05	Dynamical systems in classical and celestial mechanics
35Q53	KdV equations (Korteweg-de Vries equations)
35B10	Periodic solutions to PDEs
35Q51	Soliton equations

Keywords:

nonlinear evolution equations; Jacobi elliptic functions; hyperbolic function solutions; solitary wave solutions; trigonometric function solutions; nonlinear Schrödinger equation

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