On The Existence of Discrete Solitons in a Hexagonal Lattice

Abstract

The discrete nonlinear Schr odinger equation on a non - square hexagonal geometry lattice due to the topological charge shows the possibility of a closed phase portrait and limit cycle in case of focusing nonlinearity. A linear stability analysis of discrete solitons is presented. The method of numerical continuation is applied t o solve the dynamical equations. The phase plane analysis shows existence of Limit cycle in the phase plane indicating stability of soliton