Edge solitons in the QHE

Details Edge solitons in the QHE Edge solitons in the QHE

1999-09-13

arxiv.org/abs/math-ph/9909017v1

Physics

Mathematical Physics

Talk given by P. Horv\'athy at the meeting Nonlinearity Integrability and All That, Gallipoli (Lecce) Italy - July 1-10, 1999.

Scientific paper

The spacelike reduction of the Chern-Simons Lagrangian yields a modified Nonlinear Schr\"odinger 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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