arXiv subjects

J. -C. Yéra

Publications and source records attributed to J. -C. Yéra.

3 recordsLinked to original sources

arXiv2016

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↗

arXiv1998

An integrable time-dependent non-linear Schrödinger equation

The cubic non-linear Schrödinger equation (NLS), where the coefficient of the non-linear term can be a function $F(t,x)$, is shown to pass the Painlevé test of Weiss, Tabor, and Carnevale only for $F=(a+bt)^{-1}$, where $a$ and $b$ constants. This is explained by transforming the time-dependent system into the ordinary NLS (with $F=\const$.) by means of a time-dependent on-linear transformation, related to the conformal properties of non-relativistic space-time.

math-ph↗

arXiv1998

Vortex solutions of the Liouville equation

The most general vortex solution of the Liouville equation (which arises in non-relativistic Chern-Simons theory) is associated with rational functions, $f(z)=P(z)/Q(z)$ where $P(z)$ and $Q(z)$ are both polynomials, $°P<°Q\equiv N$. This allows us to prove that the solution depends on $4N$ parameters without the use of an index theorem, as well as the flux quantization~: $Φ=-4Nπ(sign κ)$.

hep-th↗