Simulations of the fusion of necklace-ring pattern in the complex Ginzburg–Landau equation by lattice Boltzmann method

Abstract

A lattice Boltzmann model for solving the (2+1) dimensional cubic-quintic complex Ginzburg–Landau equation (CQCGLE) is proposed. Different from the classic lattice Boltzmann models, this lattice Boltzmann model is based on uniformly distributed lattice points in a two-dimensional space, and the evolution of the model is about a spatial axis rather than time. The algorithm provides advantages similar to the lattice Boltzmann method in that it is easily adapted to complex Ginzburg–Landau equations. Numerical results reproduce the phenomena of the fusion of necklace-ring pattern and the effect of non-linearity on the soliton in the CQCGLE.