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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Defocusing NLS equation with nonzero background: Painleve asymptotics in transition region
非零背景 散焦NLS方程 过渡区 疼痛渐近
2023/5/5
Consider to the Cauchy problem of the defocusing NLS equation with a nonzero background. With the Dbar steepest descent method and double scaling limit, we obtain Painleve asymptotics in two transitio...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Defocusing NLS equation with nonzero background: Soliton resolution in soliton region
非零背景 散焦NLS方程 孤子区域 孤子分辨率
2023/5/5
Consider to the Cauchy problem of the defocusing NLS equation with a nonzero background. With the Dbar generalization of the nonlinear steepest descent method to compute the leading order approximatio...
Energy and local energy bounds for the 1-D cubic NLS equation in H^{-1/4}
Energy local energy bounds 1-D cubic NLS equation
2011/1/17
We consider the cubic Nonlinear Schr¨odinger Equation (NLS) in one space dimension, either focusing or defocusing. We prove that the solutions satisfy a-priori local in time Hs bounds in terms of the ...
A New Integrable Reduction of the Coupled NLS Equation
Multiple Scales Method Coupled nonlinear Klein-Gordon Equation Coupled NLS Equation Spectral Problem Integrable Hamiltonian system
2010/3/4
The method of multiple scales is used to derive a new integrable coupled nonlinear Schr\\"odinger equation (CNLS) as an amplitude equation from the coupled nonlinear Klein-Gordon Equation (CNKG). We a...