Existence of solutions for a system of coupled nonlinear Schrödinger equations

Paper Title:

A generalised Nehari manifold method for a class of non linear Schrödinger systems in $\mathbb{R}^3$

Published on:

28 February 2024

Primary Category:

Analysis of PDEs

Paper Authors:

Tommaso Cortopassi,

Vladimir Georgiev

Bullets

Key Details

•

Uses a generalized Nehari manifold method to prove existence of solutions

•

Considers a more general nonlinearity than prior work

•

Solutions concentrate energy around local minima of V

•

Solutions decay exponentially near local minima

•

Estimates solution energy in terms of ground state energies

Explore the topics in this paper

energy concentration

exponential decay

generalized nehari manifold

nonlinear schrodinger equations

positive solutions

AI generated summary

Existence of solutions for a system of coupled nonlinear Schrödinger equations

This paper proves the existence of positive solutions for a system of two coupled nonlinear stationary Schrödinger equations in R3 under certain conditions on the potential V and nonlinearity h. The solutions decay exponentially near local minima of V and have energy concentrating around these points as epsilon goes to 0. The proof uses a generalized Nehari manifold method that is new for this more general nonlinearity, restricting the prior work to R3.