On solutions to evolution equations defined by lattice operators

  • Takatoshi Ikegami
  • Daisuke TakahashiEmail author
  • Junta Matsukidaira
Open Access
Original Paper Area 1


We discuss a specific form of evolution equations defined by lattice operators. We give exact solutions for a class of those equations and evaluate the complexity of the solutions. Moreover we discuss the relationship between them and binary cellular automata, and analyze their asymptotic behavior utilizing the explicit expression of the solution.


Lattice operator Max-plus algebra Ultradiscretization Cellular automaton Integrable system 

Mathematics Subject Classification

39A14 06D99 37B15 68Q80 


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Copyright information

© The Author(s) 2013

Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  • Takatoshi Ikegami
    • 1
  • Daisuke Takahashi
    • 1
    Email author
  • Junta Matsukidaira
    • 2
  1. 1.Department of Applied MathematicsWaseda UniversityTokyoJapan
  2. 2.Department of Applied Mathematics and InformaticsRyukoku UniversityShigaJapan

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