论文标题
Riemann-Hilbert的方法和新的四组分非线性schrödinger方程的$ n $ -soliton解决方案
Riemann-Hilbert approach and $N$-soliton solutions for a new four-component nonlinear Schrödinger equation
论文作者
论文摘要
这项工作首先提出了一种新的四组分非线性schrödinger方程，并由Riemann-Hilbert方法进行了研究。首先，我们得出了与四个组件非线性schrödinger方程的$ 5 \ times5 $矩阵光谱问题相关的松弛对。然后，基于LAX对，我们分析了jost函数的光谱问题和分析特性，该方程的Riemann-Hilbert问题成功地从中得到了。此外，我们通过不反思解决Riemann-Hilbert问题来获得方程式的$ n $ soliton解决方案。最后，我们以$ n = 1 $和$ n = 2 $的方式得出了两个方程解决方案的特殊情况，并以图形方式分析了一个和两索顿解决方案的局部结构和动态行为。
A new four-component nonlinear Schrödinger equation is first proposed in this work and studied by Riemann-Hilbert approach. Firstly, we derive a Lax pair associated with a $5\times5$ matrix spectral problem for the four-component nonlinear Schrödinger equation. Then based on the Lax pair, we analyze the spectral problem and the analytical properties of the Jost functions, from which the Riemann-Hilbert problem of the equation is successfully established. Moreover, we obtain the $N$-soliton solutions of the equation by solving the Riemann-Hilbert problem without reflection. Finally, we derive two special cases of the solutions to the equation for $N=1$ and $N=2$, and the local structure and dynamic behavior of the one-and two-soliton solutions are analyzed graphically.
