Variable-coefficient F-expansion method and its application to nonlinear Schrödinger equation

In this paper, using the variable-coefficient F-expansion method, we present a number of Jacobian elliptic function solutions of nonlinear Schrödinger equations with variable-coefficient. Particular cases of these solutions, where the elliptic function modulus equals 1 and 0, are various localized solutions and trigonometric function solutions, respectively. Each of these solutions exists for a certain relation between the parameters of the equation. Therefore, they are particular cases of the complete set of periodic and localized solutions which may exist for this equation. In fact, they can serve as a seeding set of solutions which could be useful in other optical studies.