Abstract
We consider a stationary nonlinear Schrödinger equation with a repulsive delta-function impurity in one space dimension. This equation admits a unique positive solution and this solution is even. We prove that it is a minimizer of the associated energy on the subspace of even functions of H 1(ℝ, ℂ), but not on all H1 (ℝ, ℂ), and study its orbital stability.
Original language | English |
---|---|
Pages (from-to) | 121-136 |
Number of pages | 16 |
Journal | Discrete and Continuous Dynamical Systems |
Volume | 21 |
Issue number | 1 |
Publication status | Published - 2008 May 1 |
Externally published | Yes |
Keywords
- Dirac delta
- Nonlinear Schrödinger equation
- Stability
- Standing waves
- Variational methods
ASJC Scopus subject areas
- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics