扩展的G'/G展开法与变系数薛定谔方程的精确解

摘要

扩展了最近提出的G'/G展开法,当方程系数满足一定约束条件时,用扩展后的方法得到了变系数非线性薛定谔方程带有任意参数的精确解,包括双曲函数解、三角函数解以及有理函数解.当精确解中的参数取特殊值时,由该方程的双曲函数解得到其著名扭状孤立波解.分析结果表明:该方法直接有效,可用于研究数学、物理中其他非线性变系数演化方程.%The G'/G-expansion method proposed recently is further extended to solve nonlinear SchrOdingerrnequation with variable-coefficients. As a result,hyperbolic function solution,trigonometric function solution andrnrational solution with parameters were obtained when the coefficients of the equation satisfied certain constraintrnconditions. When the parameters were taken as special values, the well known kink-type solitary wave solutionsrnwere derived from the hyperbolic function solution. The results show that the proposed method is direct,rneffective and can be used for other nonlinear evolution equations with variable coefficients in mathematicalrnphysics.