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Title: SOLITON RESOLUTION FOR EQUIVARIANT SELF-DUAL CHERN-SIMONS-SCHRODINGER EQUATION IN WEIGHTED SOBOLEV CLASS

Abstract: We consider the self-dual Chern-Simons-Schrodinger equation (CSS) under equivariant symmetry, which is a L-2-critical equation. It is known that (CSS) admits solitons and finite-time blowup solutions. In this paper, we show soliton resolution for any solutions with equivariant data in the weighted Sobolev space H-1,H-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 Schrodinger 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.

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