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The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
The nonlinear Schrodinger (NLS) equation is a fundamental equation in the theory of integrable system and in many physical areas. In this talk, we will address several topics related to NLS equation, ...
In the statistical study of Hamiltonian PDEs out of the equilibrium (lack of invariant measures), it is a natural question to understand the transport properties for canonical Gaussian measures. The f...
In this talk, we consider normalized solutions of nonlinear Schrodinger equations in the plane when the nonlinearity satisfies an exponential critical growth. To study the normalized solutions by usin...
This talk will introduce some topics related to the study of nonlinear Schr?dinger equation on metric graphs, and then show the existence result of concentrated solutions to NLS equations on compact g...
We establish improved uniform error bounds for the time-splitting methods for the long-time dynamics of the nonlinear Schr\"odinger equation (NLSE) with weak nonlinearity. By a new technique of regula...
The concept of almost periodic functions is due to H. Bohr. The concept of rotation number is due to H. Poincaré. The Schr?dinger operator is named after E. Schr?dinger. I will present our work relate...
In this talk,I will introduce equations of nonlinear Schrodinger-type augmented by nonlinear damping terms. The nonlinear damping can prevent finite time blow-up in several situations. The solution of...
In this talk, we are concerned with the nonlinear logarithmic Schrodinger equations. When the potential satisfies a global assumption, we give the multiple solutions. When the potential satisfies a lo...
This paper is concerned with the numerical solution of the Maxwell–Schrodinger system under the temporal gauge, which describes light–matter interactions. We first propose a semidiscrete finite elemen...
利用傅里叶谱方法对空间分数阶非线性Schrodinger方程进行数值求解,并证明该格式保持了能量和质量的守恒性且无条件稳定。该方法在空间方向具有谱精度,在时间方向具有二阶精度。还对该格式进行误差分析及收敛性分析。最后通过数值实验验证了该算法的守恒性、准确性和有效性。
构造了具波动算子的非线性Schrodinger方程的一种线性化差分格式。即在守恒非线性差分格式的基础上,利用Taylor方法展开非线性项,引入小参数ε得到该方程的线性化差分格式。利用Fourier方法证明了其格式的收敛性和稳定性。最后通过数值例子验证了该方法的可信性和有效性。
应用变分方法,研究一类带限制的Schrodinger方程,证明其在一定条件下解的存在性。所获得的三个解:一个是正解,一个是负解,对于第三个解,本文只证明它的存在性,而没有确定它的正负性。
主要研究分数阶非线性Schrodinger方程的时间分裂算法,将分数阶非线性Schrodinger方程分裂成一个线性方程和一个非线性方程分别求解。其中,非线性方程可精确求解,并满足“点点守恒”,而线性方程利用CrankNicolson差分格式离散求解。证明了该算法在离散形式下保持了原方程的质量和能量的守恒性,是无条件稳定的,收敛误差为O(h2+τ2)。最后通过数值实验验证了该算法的可行性和精度...
We consider the cubic defocusing nonlinear Schr¨odinger equation in the two dimensional torus. Fix s > 1. Colliander, Keel, Staffilani, Tao and Takaoka proved in [CKS+10] the existence of solutions wi...

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