Vol. 7, No. 7, 2014

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

Xuwen Chen and Paul Smith

Vol. 7 (2014), No. 7, 1683–1712

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 that 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.

Chern–Simons–Schrödinger system, Chern–Simons–Schrödinger hierarchy, unconditional uniqueness
Mathematical Subject Classification 2010
Primary: 35Q55, 81V70, 35A02
Secondary: 35A23, 35B45
Received: 10 June 2014
Revised: 7 August 2014
Accepted: 10 September 2014
Published: 12 December 2014
Xuwen Chen
Department of Mathematics
Brown University
151 Thayer Street
Box 1917
Providence, RI 02912
United States
Paul Smith
Mathematics Department
University of California, Berkeley
Evans Hall
Berkeley, CA 94720-3840
United States
1600 Amphitheatre Parkway
Mountain View, CA 94043
United States