A Derivation of Conserved Quantities and Symmetries for the Multi-Dimensional Soliton Equations

  • K. Kajiwara
  • J. Satsuma
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)


Since the study on the KdV equation by Miura[l], it has been shown that soliton equations have the remarkable properties, the existence of an infinite number of conserved quantities and symmetries. Several methods have been proposed successfully to show these properties for the equations which have one spatial dimension[2]. However, for the higher dimensional cases or for the discrete equations, the problems are rather complicated and it is not so easy to give the explicit expressions.


Linear Problem Nonlinear Evolution Equation Nonlinear Partial Differential Equation Toda Lattice High Dimensional Case 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • K. Kajiwara
    • 1
  • J. Satsuma
    • 1
  1. 1.Department of Applied Physics, Faculty of EngineeringUniversity of TokyoBunkyo-ku, Tokyo 113Japan

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