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

Highlight
• Phenomena of the fusion of two dimensional necklace-ring patterns have been reproduced by using lattice Boltzmann model.
• The algorithm provides advantages similar to the lattice Boltzmann method in that it is easily adapted to complex Ginzburg–Landau equations.
• Numerical results show that the model can be used to simulate the soliton in the CQCGLE.

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.