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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.
      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.
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