Knot soliton solutions for the one-dimensional non-linear Schrödinger equation

Abstract

We identify that for a broad range of parameters a variant of the soliton solution of the one-dimensional non-linear Schr\"{odinger} equation, the {\it breather}, is distinct when one studies the associated space curve (or soliton surface), which in this case is knotted. The signi ficance of these solutions with such a hidden non-trivial topological element is pre-eminent on two counts: it is a one-dimensional model, and the no nlinear Schrödinger equation is well known as a model for a variety of physical systems.

5 pages, 2 figures, and 3 animation