论文标题
$ n $ -soliton fokas-lenells方程的解决方案，用于等离子体离子 - 循环波：逆散射变换方法
$N$-soliton solutions of the Fokas-Lenells equation for the plasma ion-cyclotron waves: Inverse scattering transform approach
论文作者
论文摘要
我们提出了一种简单而建设性的方法，可以找到Davydova和Lashkin建议的方程式的$ N $ -SOLITON解决方案，以描述血浆中的非线性离子 - 循环波的动力学，并随后以更通用的形式（以更通用的形式）为Fokas-lenells equartion。使用经典的反向散射转换方法，我们发现了明亮的$ n $ -soliton解决方案，理性$ n $ -soliton解决方案和$ n $ -Soliton解决方案，其形式是指数和理性功能的形式。明确的呼吸溶液作为例子。与海洛塔或darboux类型的纯代数构建体不同，我们还为无穷大的任意初始数据衰减提供了一般表达，其中包含连续光谱的贡献（辐射）。
We present a simple and constructive method to find $N$-soliton solutions of the equation suggested by Davydova and Lashkin to describe the dynamics of nonlinear ion-cyclotron waves in a plasma and subsequently known (in a more general form and as applied to nonlinear optics) as the Fokas-Lenells equation. Using the classical inverse scattering transform approach, we find bright $N$-soliton solutions, rational $N$-soliton solutions, and $N$-soliton solutions in the form of a mixture of exponential and rational functions. Explicit breather solutions are presented as examples. Unlike purely algebraic constructions of the Hirota or Darboux type, we also give a general expression for arbitrary initial data decaying at infinity, which contains the contribution of the continuous spectrum (radiation).
