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.
| Original language | English |
|---|---|
| Article number | ARTN 036704 |
| Number of pages | 9 |
| Journal | Physical Review E: Statistical, nonlinear, and soft matter physics |
| Volume | 74 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2006 |
Keywords
- ROSSBY SOLITON MODEL
- QUANTUM-MECHANICS
- WAVES
- CELLULAR-AUTOMATA
- BLOCK-EDDY INTERACTION
- GAS MODEL
Fingerprint
Dive into the research topics of 'Lattice Boltzmann schemes for the nonlinear Schrödinger equation'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver