The GL (Ginzburg–Landau) equation is a very important equation in superconductivity, which can be employed to explain many phenomena. In the present work, by using the expanded F-expansion method, some new exact Jacobi elliptic function solutions of the equation are obtained. More important is the phase factor of the solutions.
With the help of the generalized Jacobi elliptic function, an improved Jacobi elliptic function method is used to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Lin equation are investigated, and the exact solutions are derived with the aid of the homogenous balance principle.
In this paper, we use the improved modified extended tanh-function method to obtain exact solutions for the nonlinear longitudinal wave equation in magneto-electro-elastic circular rod. With the aid of this method, we get many exact solutions like bright and singular solitons, rational, singular periodic, hyperbolic, Jacobi elliptic function and exponential solutions. Moreover, the two-dimensional and the three-dimensional graphs of some solutions are plotted for knowing the physical interpretation.
Generalized Jacobi Elliptic Function Solution to a Class of Nonlinear Schrödinger-Type Equations
