Edge solitons in the QHE
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.
math-ph↗