Bright, dark and dark-singular soliton solutions of nonlinear Schr?dinger's equation with spatio-temporal dispersion

摘要

This article presents an analytical study of the propagation of solitons through optical fibres. We consider a nonlinear Schr?dinger equation with spatio-temporal dispersion and quadratic-cubic nonlinearity. Jacobi elliptic functions are used as an ansatz to extract optical dark and bright solitons as well as Jacobi elliptic solutions. The extended direct algebraic method gives dark and dark-singular soliton solutions. The constraint conditions which guarantee the existence of soliton solutions are listed.