From nonlinear Schr\"odinger equation to interacting particle system: 1 < p < 2
Analysis of PDEs
2025-10-28 v1
Abstract
We investigate the limiting behavior of solutions with infinitely many peaks to nonlinear Schr\"odinger equations [-epsilon^2 Delta u_epsilon + u_epsilon = u_epsilon^p, u_epsilon > 0 in R^n,] as epsilon -> 0, where p is Sobolev subcritical. We derive the interaction law among the limiting peak points and complete the analysis for the previously unresolved range 1 < p < 2, extending the work of Ao, Lv, and Wang (J. Differential Equations, 2025).
Keywords
Cite
@article{arxiv.2510.23128,
title = {From nonlinear Schr\"odinger equation to interacting particle system: 1 < p < 2},
author = {Xin Liao and Juntao Lv},
journal= {arXiv preprint arXiv:2510.23128},
year = {2025}
}