银河系动力学中的色散行为

The long-time asymptotic behaviors of the solutions for the coupled dispersive AB system with weighted Sobolev initial data

In this work, we employ the $\bar{\partial}$-steepset descent method to study the Cauchy problem of the coupled dispersive AB system with initial conditions in weighted Sobolev space $H^{1,1}(\mathbb{R})$, \begin{align*} \left\{\begin{aligned} &A_{xt}-αA-βAB=0,\\ &B_{x}+\fracγ{2}(|A|^2)_t=0,\\ &A(x,0)=A_0(x),~~~~B(x,0)=B_0(x)\in H^{1,1}(\mathbb{R}). \end{aligned}\right. \end{align*} Begin with the Lax pair of the coupled dispersive AB system, we successfully derive the solutions of the coupled dispersive AB system by constructing the basic Riemann-Hilbert problem. By using the $\bar{\partial}$…

Long-time Asymptotic Behavior of the coupled dispersive AB system in Low Regularity Spaces

In this paper, we mainly investigate the long-time asymptotic behavior of the solution for the coupled dispersive AB system with weighted Sobolev initial data, which allows soliton solutions via the Dbar steepest descent method.Based on the spectral analysis of Lax pair, the Cauchy problem of the coupled dispersive AB system is transformed into a Riemann-Hilbert problem, and its existence and uniqueness of the solution is proved by the vanishing lemma. The stationary phase points play an important role in the long-time asymptotic behavior. We demonstrate that in any fixed time cone $\mathcal{C…

色散估计与相互作用玻色气体玻利乌夫动力学的长期有效性

Dispersive estimates and long-time validity for Bogoliubov dynamics of interacting Bose gases

本文研究了弱相互作用玻色气体的玻利乌夫近似，并证明了该理论在所有时间尺度上的有效性，通过分析色散行为来严格推导量子涨落的有效描述。

关于Korteweg-de Vries方程色散shock waves的形式

On the form of dispersive shock waves of the Korteweg-de Vries equation

我们表明，Korteweg-de Vries冲击问题的解决方案的长期行为可以描述为一个缓慢调制的一个间隙的解决方案中的色散冲击区。椭圆函数的模（即，基础薛定谔算子的谱）仅取决于初始数据步长的大小和方向$\frac{x}{t}=const.$，沿着该方向我们确定解的渐近行为。而相移（即，狄利克雷谱）也取决于散射数据，并通过雅可比反演问题显式计算。

Hirota方程中色散激波与稀疏波的同向超车碰撞问题

The co-directional overtaking collision problem between a dispersive shock wave and a rarefaction wave for the Hirota equation

本文研究散焦Hirota方程框架下同向传播的色散激波与稀疏波的超车碰撞问题，基于Whitham理论构造初始构型，通过广义hodograph变换等得到碰撞域调制解，解析描述碰撞动力学并经数值模拟验证，为该类碰撞问题提供了详细的理论分析。

具有二次势的对数薛定谔方程

Logarithmic Schr{ö}dinger equation with quadratic potential

本文研究二次势下对数薛定谔方程的动力学，证明谐振势产生的广义高斯子孤立波轨道稳定，并刻画了部分约束与排斥势情形下的色散行为。