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 Volume 7, Number 4, 2017, Pages 1586-1597                                                                DOI：10.11948/2017096 Exact travelling wave solutions for nonlinear Schr\"{o}dinger equation with variable coefficients Xiuying Liu Keywords:Nonlinear Schr\"{o}dinger equation, travelling wave solution, extended $(\frac{G''}{G})$-expansion method. Abstract: 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. PDF      Download reader