Soliton resolution for equivariant self-dual Chern–Simons–Schrödinger equation in weighted Sobolev class
Year: 2025
Type: article
Abstract: : We consider the self-dual Chern--Simons--Schr\"{o}dinger equation (CSS) under equivariant symmetry, which is a $L^{2}$-critical equation. It is known that (CSS) admits solitons and finite-time blow-up solutions. In this paper, we show \emph{soliton resolution} for any solutions with equivariant data in the weighted Sobolev space $H^{1,1}$: every maximal solution decomposes into at most one modulated soliton and a radiation. A striking fact is that the nonscattering part must be a single modulated soliton. To our knowledge, this is the first result on soliton resolution in a class of nonlinear Schr\"{o}dinger equations which are not known to be completely integrable. The key ingredient is the defocusing nature of the equation in the exterior of a soliton profile. This is a consequence of two distinctive features of (CSS): self-duality and nonlocal nonlinearity.
Source: American Journal of Mathematics
Authors: Kihyun Kim, Soonsik Kwon, Sung-Jin Oh
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416618653