标题： 非线性薛定谔方程的大阶呼吸子 显示英文标题

标题： Large order breathers of the nonlinear Schrödinger equation

摘要： 多孤子和高阶孤子解是可积聚焦非线性薛定谔方程中两种著名的解。 多孤子的动力学自上个世纪70年代以来，通过行列式分析已为我们所熟知。 然而，关于高阶孤子的研究进展很少。 在本工作中，我们希望分析高阶呼吸子的大阶渐近行为，这些是具有与非线性薛定谔方程相同速度的双高阶孤子的特殊情况。 为了分析大阶动力学，我们首先将达布变换的表示转换为黎曼-希尔伯特问题的框架。 然后，我们通过Deift-Zhou非线性最陡下降方法表明存在五个不同的渐近区域。 有趣的是，在大阶渐近行为中首次发现了一个新的三阶亏格渐近区域，这丰富了大阶孤子领域的动态行为。 所有渐近分析的结果都通过数值方法进行了验证。 显示英文摘要

摘要： Multi-soliton and high-order soliton solutions are two type of famous ones in the integrable focusing nonlinear Schr\"odinger equation. The dynamics of multi-soliton was well known to us since 70s of the last century by the determinant analysis. However, there is few progress on the high-order solitons. In this work, we would like to analyze the large order asymptotics for the high-order breathers, which are special cases of double high-order solitons with the same velocity to the nonlinear Schr\"odinger equation. To analyze the large order dynamics, we first convert the representation of Darboux transformation into a framework of Riemann-Hilbert problem. Then we show that there exist five distinct asymptotic regions by the Deift-Zhou nonlinear steepest descent method. It is very interesting that a novel genus-three asymptotic region is first found in the large order asymptotics to large high-order breathers, which enriches the dynamic behaviors in the field of large order solitons. All results to the asymptotic analysis are verified by the numerical method.