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https://doi.org/10.1007/s40509-015-0038-6

has been cited by the following article:

• TITLE: Solution of Nonlinear Advection-Diffusion Equations via Linear Fractional Map Type Nonlinear QCA

  AUTHORS: Shinji Hamada, Hideo Sekino

  KEYWORDS: Nonlinear Quantum Cellular Automaton, QCA, Quantum Walk, Linear Fractional Map, Advection-Diffusion Equation, Burgers Equation, Porous-Medium Equation, Soliton

  JOURNAL NAME: Journal of Quantum Information Science, Vol.6 No.4, December 13, 2016

  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 Schrödinger 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.