The paper claims a curvature-corrected energy spectrum for a particle on a torus knot, but the central constant identity behind the spectrum is false.
Bright Solitary Waves on a Torus: Existence, Stability and Dynamics for the Nonlinear Schr\"odinger Model
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abstract
Motivated by recent developments in the realm of matter waves, we explore the potential of creating solitary waves on the surface of a torus. This is an intriguing perspective due to the role of curvature in the shape and dynamics of the coherent structures. We find different families of bright solitary waves for attractive nonlinearities including ones localized in both angular directions, as well as waves localized in one direction and homogeneous in the other. The waves localized in both angular directions have also been partitioned into two types: those whose magnitude decays to zero and those who do not. The stability properties of the waves are examined and one family is found to be spectrally stable while most are spectrally unstable, a feature that we comment on. Finally, the nature of the ensuing nonlinear dynamics is touched upon.
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hep-th 1years
2019 1verdicts
REJECT 1representative citing papers
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Quantum Mechanics of Particle on a torus knot: Curvature and Torsion Effects
The paper claims a curvature-corrected energy spectrum for a particle on a torus knot, but the central constant identity behind the spectrum is false.