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Edge solitons in the QHE

M. Hassaïne P. A. Horváthy·J. -C. Yéra
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Abstract

The spacelike reduction of the Chern-Simons Lagrangian yields a modified Nonlinear Schrödinger Equation (jNLS) where in the non-linearity the particle density is replaced by current. When the phase is linear in the position, this latter is an ordinary NLS with time-dependent coefficients which admits interesting solutions, whose arisal is explained by the conformal properties of non-relativistic spacetime. However, only the usual travelling soliton is consistent with the jNLS. Adding a six-order potential converts jnLS into an integrable equation.

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M. Hassaïne P. A. Horváthy, J. -C. Yéra. 2016-08-15. Edge solitons in the QHE. https://arxiv.org/abs/math-ph/9909017

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