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arXiv · 1406.2649

On the unconditional uniqueness of solutions to the infinite radial Chern-Simons-Schrödinger hierarchy

Xuwen Chen·Paul Smith
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Abstract

In this article we establish the unconditional uniqueness of solutions to an Infinite Radial Chern-Simons-Schrödinger (IRCSS) hierarchy in two spatial dimensions. The IRCSS hierarchy is a system of infinitely many coupled PDEs that describes the limiting Chern-Simons-Schrödinger dynamics of infinitely many interacting anyons. The anyons are two dimensional objects which interact through a self-generated field. Due to the interactions with the self-generated field, the IRCSS hierarchy is a system of nonlinear PDEs, which distinguishes it from the linear infinite hierarchies studied previously. Factorized solutions of the IRCSS hierarchy are determined by solutions of the Chern-Simons-Schrödinger system. Our result therefore implies the unconditional uniqueness of solutions to the radial Chern-Simons-Schrödinger system as well.

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Xuwen Chen, Paul Smith. 2014-09-11. On the unconditional uniqueness of solutions to the infinite radial Chern-Simons-Schrödinger hierarchy. https://doi.org/10.2140/apde.2014.7.1683

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