中文摘要：

人们一直以来对于含五次方的一维非线性薛定谔方程的求解问题感兴趣,但是只获得了由椭圆函数和双曲函数组成的有限多个新解。为了获得含五次方的一维非线性薛定谔方程的无穷序列新解,对该方程进行了一系列变换,从而利用RIccati方程的Backlund变换和解的非线性叠加公式等相关结论,构造了含五次方的一维非线性薛定谔方程的由三角函数、双曲函数和有理函数组成的无穷序列新精确解。

英文摘要：

People are always interested in solving the problem of one-dimensional nonlinear Schr5dinger equation with the fifth power. However, only a limited number of new solutions consisting of the elliptic and hyperbolic functions were obtained. In order to obtain a new infinite sequence solutions of one-dimensional nonlinear SchrSdinger equation with fifth power, it makes a series of transformations on the equation, and using the related conclusions of B~cklund transform and nonlinear superposition formula of Riccati equation the new infinite sequence solutions of one-dimensional nonlinear SchrSdinger equation with the fifth power consisting of trigonometric function, hyperbolic function and rational function were constructed.