论文标题
非线性schrödinger方程的大订单呼吸器
Large order breathers of the nonlinear Schrödinger equation
论文作者
论文摘要
在可集成的焦点非线性schrödinger方程中，多氧化和高级孤子解决方案是两种著名的解决方案。自上世纪70年代以来，我们众所周知，多索顿的动力学通过决定性分析。但是，高阶孤子的进展很少。在这项工作中，我们想分析高阶呼吸器的大级渐近学，这是具有与非线性Schrödinger方程相同速度的双重高阶孤子子的特殊情况。为了分析大阶动力学，我们首先将Darboux转换的表示形式转换为Riemann-Hilbert问题的框架。然后我们表明，通过Deift-Zhou非线性最陡的下降方法存在五个不同的渐近区域。有趣的是，首先在大型高阶呼吸器上首先发现了一个新型的三个渐近区域，这富含大阶孤子领域的动态行为。通过数值方法验证了渐近分析的所有结果。
Multi-soliton and high-order soliton solutions are two type of famous ones in the integrable focusing nonlinear Schrödinger 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 Schrödinger 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.
