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Exact solutions to nonlinear Schrödinger equation with variable coefficients. (English) Zbl 1210.35201
Summary: According to Ma-Fuchsseiter’s idea, a trial equation method was proposed to find the exact envelop traveling wave solutions to some nonlinear differential equations with variable coefficients. As an application, combining with the complete discrimination system for polynomial, some exact envelop traveling wave solutions to Schrödinger equation with variable coefficients were obtained. At the same time, the physical meanings of the obtained solutions are discussed, and the problem needed to further study is pointed out.
35Q51Soliton-like equations
35Q53KdV-like (Korteweg-de Vries) equations
35Q55NLS-like (nonlinear Schrödinger) equations
35C07Traveling wave solutions of PDE
35A24Methods of ordinary differential equations for PDE
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