Hierarchy of soliton solutions to the gauged nonlinear Schrödinger equation on the plane
- 24 December 1990
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 65 (26) , 3230-3232
- https://doi.org/10.1103/physrevlett.65.3230
Abstract
We find static, self-dual solutions to the SU(N) gauged, nonlinear Schrödinger equation in two spatial dimensions with scalar matter in the adjoint representation. The gauge field is determined dynamically by the Chern-Simons interaction with nonrelativistic scalar matter. The hierarchy is associated with the Toda hierarchy, which can be solved explicitly. The N=2 case reduces to the Liouville equation found by Jackiw and Pi, when looking at the nonlinear Schrödinger equation gauged by U(1).Keywords
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