From nonlinear Schrödinger equation to interacting particle system

We study the limiting behavior of solutions to nonlinear Schr & ouml;dinger 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. These solutions are assumed to have infinitely many peaks. We derive the interaction form between the limiting peak points. This is achieved by first describing the main order term of u pound and providing a very precise estimate on the error by the reverse Lyapunov-Schmidt reduction method, and then extracting information from the reduction equation in a limiting way. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.