论文标题
六个非线性schrödinger方程的逆散射变换和多彩色溶液
Inverse scattering transform and multi-solition solutions for the sextic nonlinear Schrödinger equation
论文作者
论文摘要
在这项工作中，我们考虑了六个非线性schrödinger方程的反散射变换和多彩色溶液。频谱问题的JOST函数是直接得出的，并根据分析JOST函数的对称性和其他相关属性获得了具有$ t = 0 $的散射数据。然后，我们利用翻译转换来获得电势和内核之间的关系，并根据Gel'fand-Levitan-Marchenko（GLM）积分方程收回潜力。此外，在基本的基础上考虑了散射数据的时间演变，得出了多彩色溶液。此外，分析了方程的某些解决方案并通过图形分析揭示了其动态行为，这可以丰富六个非线性schrödinger方程的非线性现象。
In this work, we consider the inverse scattering transform and multi-solition solutions of the sextic nonlinear Schrödinger equation. The Jost functions of spectrum problem are derived directly, and the scattering data with $t=0$ are obtained according to analyze the symmetry and other related properties of the Jost functions. Then we take use of translation transformation to get the relation between potential and kernel, and recover potential according to Gel'fand-Levitan-Marchenko (GLM) integral equations. Furthermore, the time evolution of scattering data is considered, on the basic of that, the multi-solition solutions are derived. In addition, some solutions of the equation are analyzed and revealed its dynamic behavior via graphical analysis, which could be enriched the nonlinear phenomena of the sextic nonlinear Schrödinger equation.
