title: Lattice Boltzmann schemes for the nonlinear Schrödinger equation.
abstract: The lattice Boltzmann (LB) method is applied to solve the time-dependent nonlinear Schrödinger (NLS) equation. Through approximating the reaction term at different orders of accuracy, three diffusion-reaction LB schemes are constructed for the cubic NLS equation. A LB initial condition is proposed to include the first-order nonequilibrium distribution function. These LB schemes are used to solve the one-soliton propagation and the homoclinic orbit problems. Detailed simulation results confirm that the high-order reaction term and the LB initial condition are effective in reducing the truncation errors. Compared with the Crank-Nicolson finite difference scheme, the LB scheme is found to give at least comparable and generally more accurate approximation for the cubic NLS equation.
authors.affiliation: Laboratory of Cloud-Precipitation Physics and Severe Storms (LACS), Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029, China. zlh@mail.iap.ac.cn
authors.forename: Linhao
authors.initials: L
authors.lastname: Zhong
authors.forename: Shide
authors.initials: S
authors.lastname: Feng
authors.forename: Ping
authors.initials: P
authors.lastname: Dong
authors.forename: Shouting
authors.initials: S
authors.lastname: Gao