Exact travelling wave solutions for nonlinear Schr\"{o}dinger equation with variable coefficients

In this paper, two nonlinear Schr\"{o}dinger equations with variable coefficients in nonlinear optics are investigated. Based on travelling wave transformation and the extended $(\frac{G''}{G})$-expansion method, exact travelling wave solutions to nonlinear Schr\"{o}dinger equation with time-dependent coefficients are derived successfully, which include bright and dark soliton solutions, triangular function periodic solutions, hyperbolic function solutions and rational function solutions.