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On the unconditional
uniqueness of solutions to the infinite radial
Chern–Simons–Schrödinger hierarchy
Xuwen Chen and Paul Smith |
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Vol. 7 (2014), No. 7, 1683–1712
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Abstract |
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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. |
Keywords
Chern–Simons–Schrödinger system, Chern–Simons–Schrödinger
hierarchy, unconditional uniqueness
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Mathematical Subject Classification 2010
Primary: 35Q55, 81V70, 35A02
Secondary: 35A23, 35B45
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Milestones
Received: 10 June 2014
Revised: 7 August 2014
Accepted: 10 September 2014
Published: 12 December 2014
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Authors |
| Xuwen Chen | |
| Department of Mathematics Brown University 151 Thayer Street Box 1917 Providence, RI 02912 United States |
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| Paul Smith | |
| Mathematics Department University of California, Berkeley Evans Hall Berkeley, CA 94720-3840 United States |
Google 1600 Amphitheatre Parkway Mountain View, CA 94043 United States |
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