女王调教

徐桂香，北京师范大学女王调教 教授。在位势波动方程孤子猜想、导数NLS方程多孤子解的稳定性、耦合非线性相互作用薛定谔方程解的整体适定性与散射、Hartree方程解长时间动力学行为、高阶能量临界NLS方程解的整体适定与散射、质量临界NLS及KdV方程解的低正则性理论等方面与合作者做了一些工作。系列学术论文被接收发表在Amer. J. Math., Comm. Math. Phys.,  J. Funct. Anal.,  J. Math. Pures Appl. , Ann I. H. Poincaré, AN. ,  IMRN,  Comm. PDEs. ,  SIAM J. Math. Anal. ,  Forum Math. ,  J. Diff. Equat，Dynamics of PDEs,  Canada J. Math.等学术期刊。

 

Abstract: We will survey the recent developments about the stability of the solitary waves for the (generalized) derivative Schrodinger equation. We firstly show the existence/nonexistence of traveling waves for NLS with derivative (DNLS) by the structure analysis, ODE argument and the variational argument.  Secondly, we consider the orbital stability of the solitary waves for the derivative Schrodinger equation in the energy space. Last, we will show the orbital instability of the solitary waves for the generalized derivative Schrodinger equation in the degenerate case. They are joint works with Prof. Changxing Miao and Xingdong Tang.