Article

# Quantum lattice gas representation of some classical solitons

Department of Electrical & Computer Engineering, Old Dominion University, Norfolk, VA 23529, USA

Physics Letters A (Impact Factor: 1.63). 04/2003; DOI: 10.1016/S0375-9601(03)00334-7 - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, a lattice Boltzmann model for the three-dimensional complex Ginzburg–Landau equation is proposed. The multi-scale technique and the Chapman–Enskog expansion are used to describe higher-order moments of the complex equilibrium distribution function and a series of complex partial differential equations. The modified partial differential equation of the three-dimensional complex Ginzburg–Landau equation with the third order truncation error is obtained. Based on the complex lattice Boltzmann model, some motions of the stable scroll, such as the scroll wave with a straight filament, scroll ring, and helical scroll are simulated. The comparisons between results of the lattice Boltzmann model with those obtained by the alternative direction implicit scheme are given. The numerical results show that this model can be used to simulate the three-dimensional complex Ginzburg–Landau equation.Journal of Scientific Computing 09/2013; · 1.70 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**A lattice Boltzmann model for the bimolecular autocatalytic reaction-diffusion equation is proposed. By using multi-scale technique and the Chapman-Enskog expansion on complex lattice Boltzmann equation, we obtain a series of complex partial differential equations, complex equilibrium distribution function and its complex moments. Then, the complex reaction-diffusion equation is recovered with higher-order accuracy of the truncation error. This equation can be used to describe the bimolecular autocatalytic reaction-diffusion systems, in which a rich variety of behaviors have been observed. Based on this model, the Fitzhugh-Nagumo model and the Gray-Scott model are simulated. The comparisons between the LBM results and the Alternative Direction Implicit results are given in detail. The numerical examples show that assumptions of source term can be used to raise the accuracy of the truncation error of the lattice Boltzmann scheme for the complex reaction-diffusion equation.Applied Mathematical Modelling 05/2014; · 2.16 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, a higher-order accuracy lattice Boltzmann model for the complex Ginzburg-Landau equation is proposed. In order to obtain higher-order accuracy of truncation error and to overcome the drawbacks of “error rebound” in the previous models, a new assumption of additional distribution is presented to improve the accuracy of the model for the complex partial differential equation with nonlinear source term. As results, the complex Ginzburg-Landau equation is recovered with the fourth-order accuracy of truncation error. Based on this model, the problems of a single spiral wave in two-dimensional (2D) space and a single scroll in three-dimensional (3D) space are implemented to test the lattice Boltzmann scheme. The comparisons between the LBM results and the Alternative Direction Implicit results are given in detail. The numerical examples show that assumptions of source term can be used to raise the accuracy of the truncation error of the lattice Boltzmann scheme for the complex Ginzburg-Landau equation.Journal of Scientific Computing 01/2012; 52(3). · 1.70 Impact Factor

Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.