Nonlinear Evolution Equations, Inverse Scattering and Cellular Automata

  • Mark J. Ablowitz
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 25)


There is a class of nonlinear evolution equations which have solitons as special solutions. Significantly many of these equations fall into a class for which the Inverse Scattering Transform method applies. A discussion of this method of solution for certain prototype nonlinear evolution equations in continuous media in 1 + 1 and 2 + 1 dimensions is given. It also turns out that there are cellular automata which admit soliton solutions and have many similar properties, but there are significant differences as well. One of these cellular automata is discussed in some detail.


Solitary Wave Cellular Automaton Soliton Solution Cellular Automaton Nonlinear Evolution Equation 
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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Mark J. Ablowitz
    • 1
  1. 1.Program in Applied MathematicsUniversity of Colorado at BoulderUSA

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