The solution of the nonlinear Schr?dinger equation using Lattice- Boltzmann

21st Latin American Symposium on Solid State Physics

Fonseca, F.^1

Universidad Nacional de Colombia, Departamento de Física, Ciudad Universitaria, Bogotá Av. Cra. 30 No 45-03, Colombia^1

关键词: Complex components;    Complex valued functions;    Dinger equation;    Lattice boltzmann;    Lattice Boltzmann method;    Nonlinear coupling;    Stable structures;    Symmetric tensors;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/480/1/012037/pdf
DOI  :  10.1088/1742-6596/480/1/012037

来源: IOP

【 摘 要 】

We present the solution of the nonlinear Schrodinger equation using the lattice Boltzmann method. We show results for two dimensions using a d2q9 lattice velocity scheme. To implement the expansion B.G.K. (Bhatnagar-Gross- Krook), we assume the distribution function as a complex valued function, whose real and complex components satisfy the Boltzmann equation. The strategy followed to obtain the motion equation is to define adequately the second moment of the distribution as a symmetric tensor. We obtain stable structures for given values of the nonlinear coupling constant.