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Solution of Nonlinear Advection-Diffusion Equations via Linear Fractional Map Type Nonlinear QCA
Toyohashi University of Technology, Toyohashi, Japan
Stony Brook University, New York, USA
Tokyo Institute of Technology, Tokyo, Japan
- 1 Toyohashi University of Technology, Toyohashi, Japan
- 2 Stony Brook University, New York, USA
- 3 Tokyo Institute of Technology, Tokyo, Japan
Journal of Quantum Information Science·Volume 06 (2016)·Pages 263–295·Published 31 October 2016·DOI10.4236/jqis.2016.64017
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Abstract
Linear fractional map type (LFMT) nonlinear QCA (NLQCA), one of the simplest reversible NLQCA is studied analytically as well as numerically. Linear advection equation or Time Dependent Schr ö dinger Equation (TDSE) is obtained from the continuum limit of linear QCA. Similarly it is found that some nonlinear advection-diffusion equations including inviscid Burgers equation and porous-medium equation are obtained from LFMT NLQCA.
KeywordsNonlinear Quantum Cellular AutomatonQCAQuantum WalkLinear Fractional MapAdvection-Diffusion EquationBurgers EquationPorous-Medium EquationSoliton
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