Optical solitons in nematic liquid crystals: model with saturation effects

BORGNA, JUAN PABLO; PANAYOTAROS, PANAYOTIS; RIAL, DIEGO; DE LA VEGA, CONSTANZA SÁNCHEZ F

NONLINEARITY

IOP PUBLISHING LTD

Año: 2018 vol. 31 p. 1535 - 1559

0951-7715

We study a 2D system that couples a Schrödinger evolution equationto a nonlinear elliptic equation and models the propagation of a laserbeam in a nematic liquid crystal. The nonlinear elliptic equationdescribes the response of the director angle to the laser beam electricfield. We obtain results on well-posedness and solitary wave solutionsof this system, generalizing results for a well-studied simpler systemwith a linear elliptic equation for the director field. The analysis ofthe nonlinear elliptic problem shows the existence of an isolated globalbranch of solutions with director angles that remain bounded forarbitrary electric field. The results on the director equation are alsoused to show local and global existence, as well as decay for initialconditions with sufficiently small L 2-norm. Forsufficiently large L 2-norm we show the existence ofenergy minimizing optical solitons with radial, positive and monotoneprofiles.