论文标题
对海洛塔方程的高阶孤子的渐近分析
Asymptotic analysis of high order soliton for the Hirota equation
论文作者
论文摘要
在本文中，我们主要分析用于海洛塔方程的高阶孤子的长期渐近学。给出了带有高阶孤子的Darboux矩阵的两个不同的Riemann-Hilbert表示，以建立反散射方法与Darboux变换之间的关系。具有单光谱参数的渐近分析通过行列式的公式直接得出。此外，通过将迭代的darboux矩阵和高级孤子与单光谱参数相结合，具有$ k $频谱参数的长期渐近学参数，该参数清楚地揭示了高阶Soliton的结构，并且可以在光学实验中使用。
In this paper, we mainly analyze the long-time asymptotics of high-order soliton for the Hirota equation. Two different Riemann-Hilbert representations of Darboux matrix with high-order soliton are given to establish the relationships between inverse scattering method and Darboux transformation. The asymptotic analysis with single spectral parameter is derived through the formulas of determinant directly. Furthermore, the long-time asymptotics with $k$ spectral parameters is given by combining the iterated Darboux matrix and the result of high-order soliton with single spectral parameter, which discloses the structure of high-order soliton clearly and is possible to be utilized in the optic experiments.
