一个新的Hamiltonian振幅方程的周期波解

Periodic wave solutions for a new Hamiltonian amplitude equation

由扩展的F-展开法获得了一个新的Hamiltonian振幅方程的新形式的周期波解.在极限情形得到了由双曲函数和三角函数表示的解.作为特别情形,得到了非线性Schrǒdinger方程的相应解.

The new form periodic wave solutions for a new Hamiltonian amplitude equation are obtained by the extended F-expansion method. We can simultaneously obtain many periodic wave solutions expressed by various Jacobi elliptic functions for the new Hamiltonian amplitude equation introduced by M. Wadati et al. In the limit case, the hyperbolic function solutions and trigonometric function solutions are given, respectively. Especially, when the parameter ε goes to zero, the new Hamiltonian amplitude equation becomes the well-known nonlinear Schr6dinger （NLS） equation, whose solutions can be derived from the solutions of the new Hamiltonian amplitude equation.