Orbital stability of ground states for a Sobolev critical Schrödinger equation

Ja n 20 04 Schrödinger equation with critical Sobolev exponent

The Fourth-Order Dispersive Nonlinear Schrödinger Equation: Orbital Stability of a Standing Wave

Considered in this report is the one-dimensional fourth-order dispersive cubic nonlinear Schrödinger equation with mixed dispersion. Orbital stability, in the energy space, of a particular standing-wave solution is proved in the context of Hamiltonian systems. The main result is established by constructing a suitable Lyapunov function.

Approximate Solutions of the Nonlinear Schrödinger Equation for Ground and Excited States of Bose-Einstein Condensates

I present simple analytical methods for computing the properties of ground and excited states of Bose-Einstein condensates, and compare their results to extensive numerical simulations. I consider the effect of vortices in the condensate for both positive and negative scattering lengths, a, and find an analytical expression for the large-N0 limit of the vortex critical frequency for a > 0, by a...

Ground States for the Fractional Schrödinger Equation

In this article, we show the existence of ground state solutions for the nonlinear Schrödinger equation with fractional Laplacian (−∆)u+ V (x)u = λ|u|u in R for α ∈ (0, 1). We use the concentration compactness principle in fractional Sobolev spaces Hα for α ∈ (0, 1). Our results generalize the corresponding results in the case α = 1.

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 ...