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arXiv · 2510.23128

From nonlinear Schr\"odinger equation to interacting particle system: 1 < p < 2

Xin Liao·Juntao Lv
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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).

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Xin Liao, Juntao Lv. 2025-10-27. From nonlinear Schr\"odinger equation to interacting particle system: 1 < p < 2. https://arxiv.org/abs/2510.23128

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