Finite Time Extinction by Nonlinear Damping for the Schrödinger Equation

Finite time extinction by nonlinear damping for the Schrodinger equation

We consider the Schrödinger equation on a compact manifold, in the presence of a nonlinear damping term, which is homogeneous and sublinear. For initial data in the energy space, we construct a weak solution, defined for all positive time, which is shown to be unique. In the one-dimensional case, we show that it becomes zero in finite time. In the two and three-dimensional cases, we prove the s...

An exponential time differencing method for the nonlinear Schrödinger equation

The spectral methods offer very high spatial resolution for a wide range of nonlinear wave equations, so, for the best computational efficiency, it should be desirable to use also high order methods in time but without very strict restrictions on the step size by reason of numerical stability. In this paper we study the exponential time differencing fourth-order Runge-Kutta (ETDRK4) method; thi...

Collapse of solitary excitations in the nonlinear Schrödinger equation with nonlinear damping and white noise.

Numerical solution for one-dimensional independent of time Schrödinger Equation

In this paper, one of the numerical solution method of one- particle, one dimensional timeindependentSchrodinger equation are presented that allows one to obtain accurate bound state eigenvalues and functions for an arbitrary potential energy function V(x).For each case, we draw eigen functions versus the related reduced variable for the correspondingenergies. The paper ended with a comparison ...

Stroboscopic Averaging for the Nonlinear Schrödinger Equation

In this paper, we are concerned with an averaging procedure, – namely Stroboscopic averaging [SVM07, CMSS10] –, for highly-oscillatory evolution equations posed in a (possibly infinite dimensional) Banach space, typically partial differential equations (PDEs) in a high-frequency regime where only one frequency is present. We construct a highorder averaged system whose solution remains exponenti...