Dynamics of solitons with periodic loops intrinsic localized modes and modulational instability in a quantum 2D nonlinear square Klein-Gordon chain

Abstract

Abstract We investigate the effects of dispersion and nonlinearity interactions in view of generation of nonlinear intrinsic localized modes (ILMs) and modulational instability (MI) of a quantum 2D Klein-Gordon chain. For this, using Glauber’s coherent state representation and multiple-scale method, we find that the system supports nonlinear excitations referred to bright, dark radial symmetric and bright, dark bilateral symmetric line non-traveling and traveling ILMs. We also find that moving bright and radial solution are evolving like localized periodic loops, which is very interesting in this work. By means of linear stability approach, the instability criteria, threshold amplitude, instability areas showing the generation of bright ILMs predicted to be unstable and growth rate of unstable modes in the system are obtained. Numerical investigations are performed to support the analytical analysis, and an excellent agreement with the analytical results has been found.