非等谱Davey-Stewartson I（DSI）方程中的爆炸衰变dromion

Davey-Stewartson-1方程的Dromion微扰

Dromion perturbation for the Davey-Stewartson-1 equations

研究了Davey-Stewartson-1方程dromion的长时间扰动。

四分之一平面上具有齐次Dirichlet边界条件的Davey-Stewartson I方程

The Davey-Stewartson I Equation on the Quarter Plane with Homogeneous Dirichlet Boundary Conditions

Dromion是二维空间中由非线性可积演化方程支持的指数局域相干结构。在平面上的初值问题研究中，只有当在无穷远处施加非平凡边界条件时才会出现这样的解，这种情况的物理意义是可疑的。然而，它是建立在这里，dromion自然出现在边值问题的研究。特别地，证明了具有任意初始条件和零Dirichlet边界条件的Davey-Stewartson I方程在四分之一平面上的解的长时间渐近性是由dromion支配的.非零Dirichlet边界条件的情况也进行了讨论。

A Nonlinear Plancherel Theorem with Applications to Global Well-Posedness for the Defocusing Davey-Stewartson Equation and to the Inverse Boundary Value Problem of Calderón

We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse Scattering method for the defocusing Davey-Stewartson II equation. We then use it to prove global well-posedness and scattering in $L^2$ for defocusing DSII. This Plancherel theorem also implies global uniqueness in the inverse boundary value problem of Calderón in dimension $2$, for conductivities $σ>0$ with $\log σ\in \dot H^1$. The proof of the nonlinear Plancherel theorem includes new estimates on classical fractional integrals, as well as a new result on $L^2$-boundedness of pseudo-dif…

奇摄动DSII方程的Melnikov分析

Melnikov Analysis for Singularly Perturbed DSII Equation

对Davey-Stewartson II方程在奇异扰动下进行了严格的Melnikov分析.建立了不稳定纤维定理和中心稳定流形定理。通过达布变换得到的未扰动同宿轨道是一个经典解，这一事实导致了只有局部适定性对于Melnikov测量是必要的结论。