论文标题
Riemann-Hilbert方法和N-Soliton公式用于N-组件Fokas-Lenells方程
Riemann-Hilbert approach and N-soliton formula for the N-component Fokas-Lenells equations
论文作者
论文摘要
在这项工作中，首先通过riemann-hilbert（RH）方法研究了这项工作，由Guo and Ling（2012 J.Math。53（7）073506）以$ n = 2 $进行了研究。这样做的主要目的是研究任何正整数$ n $的耦合fokas-lenells（FL）方程的孤子溶液，它们的线性关系比以前报道的类似物更复杂。我们首先分析了与$（n+1）\ times（n+1）$ n $ - 组件FL方程相关的LAX对的光谱分析。然后，成功提出了一种RH问题。通过引入不规则性和无反射情况的特殊条件，方程式的$ n $ soliton解决方案公式是通过解决相应的RH问题得出的。此外，用一些图形分析讨论了$ n = 2,3 $和$ 4 $的示例，唯一的结构和动态传播行为及其相互作用。
In this work, the generalized $N$-component Fokas-Lenells(FL) equations, which have been studied by Guo and Ling (2012 J. Math. Phys. 53 (7) 073506) for $N=2$, are first investigated via Riemann-Hilbert(RH) approach. The main purpose of this is to study the soliton solutions of the coupled Fokas-Lenells(FL) equations for any positive integer $N$, which have more complex linear relationship than the analogues reported before. We first analyze the spectral analysis of the Lax pair associated with a $(N+1)\times (N+1)$ matrix spectral problem for the $N$-component FL equations. Then, a kind of RH problem is successfully formulated. By introducing the special conditions of irregularity and reflectionless case, the $N$-soliton solution formula of the equations are derived through solving the corresponding RH problem. Furthermore, take $N=2,3$ and $4$ for examples, the localized structures and dynamic propagation behavior of their soliton solutions and their interactions are discussed by some graphical analysis.
