Transformations and Soliton Solutions for a Variable-coefficient Nonlinear Schrödinger Equation in the Dispersion Decreasing Fiber with Symbolic Computation

Describing the dispersion decreasing fiber, a variable-coefficient nonlinear Schrödinger equation is hereby under investigation. Three transformations have been obtained from such a equation to the known standard and cylindrical nonlinear Schrödinger equations with the relevant constraints on the variable coefficients presented, which turn out to be more general than those previously published in the literature. Meanwhile, several families of exact dark-soliton-like and bright-soliton-like solutions are constructed. Also, we obtain some similarity solutions, which can be illustrated in terms of the elliptic and the second Painlevé transcendent equations.