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.