Solitons in combined linear and nonlinear lattice potentials

Solitons in combined linear and nonlinear lattice potentials

Seminar author:Boris A. Malomed

Event date and time:02/17/2010 02:00:pm

Event location:IFAE seminar room

Event contact:

We study ordinary solitons and gap solitons (GSs) in the framework of the one-dimensional Gross-Pitaevskii equation (GPE) with a combination of linear and nonlinear lattice potentials. The main points of the analysis are effects of (in)commensurability between the lattices, development of analytical methods, viz., the variational approximation (VA) for narrow ordinary solitons, and various forms of the averaging method for broad solitons of both types, and also the study of mobility of the solitons. Under the direct commensurability (equal periods of the lattices), the family of ordinary solitons is similar to its counterpart in the GPE without external potentials. In the case of the subharmonic commensurability, with the period of the linear lattice equal to half of the period of the nonlinear lattice, or incommensurability, there is an existence threshold for the ordinary solitons. GS families demonstrate a bistability, unless the direct commensurability takes place. The solitons can be readily set in motion by kicking and feature inelastic collisions. The stability of the ordinary solitons is fully determined by the VK (Vakhitov-Kolokolov) criterion, i.e., a negative slope in the dependence between the solitons’s chemical potential and norm N. The stability of GS families obeys an inverted (“anti-VK”) criterion, which is explained by means of an approximation based on the averaging method. The present system provides for a unique possibility to check the anti-VK criterion, as the dependences of the chemical potential versus N for GSs feature turning points, except for the case of the direct commensurability. (Phys. Rev. A 81, 013624 (2010))