We investigate, theoretically and numerically, the modulational instability of plane waves in weakly cubic-quintic nonlocal nonlinear media. Theoretically, the Lenz transformation and the linear stability analysis are used to study the impact of cubic and quintic nonlocalities on modualtional instability through the stability diagram in different modes of nonlinearity. Moreover, the time-dependent criterion predicting the existence of the modulational instability for any value of the wave number is expressed. In the numerical part, the direct integration of the nonlinear Schrödinger equation, with the split-step method, shows the disintegration dynamics of plane wave in weakly quintic media. Theoretical predictions are in good agreement with numerical results. Particularly, the impact of the cubic and quintic nonlocalities on modulational instability is such that higher values of the quintic nonlocality contribute to reduce the modulational instability in the system. Moreover, the three-body interaction in the model gives rise to Akhmediev breathers, which are the nonlinear manifestation of modulational instability.
|Communications in Nonlinear Science and Numerical Simulation
|Published - Jan 1 2020
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Modelling and Simulation
- Applied Mathematics