论文标题
在可集成的分数耦合方程中的无孤子
Nondegenerate solitons in the integrable fractional coupled Hirota equation
论文作者
论文摘要
在本文中，基于Ablowitz提出的非线性分数方程，在Riesz分数衍生物的意义上是和Carr，我们探索了分数耦合的Hirota方程并给出其显式形式。与先前的非线性分数方程不同，这种非线性分数方程是可以集成的。因此，我们通过在无反射情况下通过反向散射转换来获得分数耦合的Hirota方程的分数$ n $ soliton溶液。特别是，我们分析了分数耦合的Hirota方程的单溶剂和两个固体溶液，并证明分数两溶液也可以被视为两个分数单词孔的线性叠加，为$ | t | \ t | \ to \ infty $。此外，在一些特殊的约束下，我们还获得了非等级分数孤子解决方案，并为它们提供了简单的分析。
In this paper, based on the nonlinear fractional equations proposed by Ablowitz, Been, and Carr in the sense of Riesz fractional derivative, we explore the fractional coupled Hirota equation and give its explicit form. Unlike the previous nonlinear fractional equations, this type of nonlinear fractional equation is integrable. Therefore, we obtain the fractional $n$-soliton solutions of the fractional coupled Hirota equation by inverse scattering transformation in the reflectionless case. In particular, we analyze the one- and two-soliton solutions of the fractional coupled Hirota equation and prove that the fractional two-soliton can also be regarded as a linear superposition of two fractional single solitons as $|t|\to\infty$. Moreover, under some special constraint, we also obtain the nondegenerate fractional soliton solutions and give a simple analysis for them.
