Knot soliton solutions for the one-dimensional non-linear Schr\"{o}dinger equation.
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 Schr\"{o}dinger equation is well known as a model for a variety of physical systems.
Publisher URL: http://arxiv.org/abs/1711.03318
DOI: arXiv:1711.03318v1
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