Lattice Boltzmann model for the interaction of (2+1)-dimensional solitons in generalized Gross–Pitaevskii equation

• A new (2+1)-dimensional generalized Gross–Pitaevskii equation is constructed.
• A lattice Boltzmann model for generalized Gross–Pitaevskii equation is proposed.
• The interaction of two (2+1)-dimensional solitons is simulated by using the LBM.

In this paper, a new lattice Boltzmann model for the interaction of two solitons in (2+1)-dimensional generalized Gross–Pitaevskii equation is proposed. By using the Chapman–Enskog expansion and the multi-scale time expansion, a series of partial differential equations in different time scales are obtained. By selecting the appropriate higher-order moments of equilibrium distribution functions, the macroscopic equation can be recovered. A numerical example is given to test the scheme. Numerical experiments demonstrate the lattice Boltzmann method is an appropriate tool to simulate the interaction of (2+1)-dimensional solitons.