一类空间分数阶非线性SchrO¨dinger方程的李群约化
Lie Group Reduction for a Kind of Space-Fractional Order Nonlinear SchrO¨dinger Equation
摘要: 本文将李群约化方法应用于一类空间分数阶非线性Schrödinger方程，得到了方程的单参数新解，以及李对称约化方程。进一步，通过求解李对称约化方程获得了空间分数阶非线性Schrödinger方程的一些群不变解和行波解。
Abstract: This paper will apply the Lie group reduction method to a kind of space-fractional order nonlinear Schrödinger equation. New single parameter solutions and reduced equations of Lie symmetry are obtained for the equation. Moreover, by solving the reduced equation of Lie symmetry, some group-invariant solutions and travelling wave solutions are given for the space-fractional order nonlinear Schrödinger equation.
文章引用：周春红, 化存才. 一类空间分数阶非线性SchrO¨dinger方程的李群约化[J]. 应用数学进展, 2016, 5(2): 310-319. http://dx.doi.org/10.12677/AAM.2016.52039

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