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On the Lax representation for the nonlinear evolution equations

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Czechoslovak Journal of Physics B Aims and scope

Abstract

By the classical differential geometry techniques it is shown that a general partial differential equation of the second order with two independent variables can be represented in the Lax operator form [X 1 X 2]=0, whereX i =∂/∂x i −Ω i,i=1,2 andΩ i are the 3×3 matrices. The problem of the introduction of the spectral parameter in this representation is shortly discussed.

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Authors and Affiliations

  1. Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, SU-141980, Dubna, USSR

    V. V. Nesterenko

Authors
  1. V. V. Nesterenko
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Additional information

The author is pleased to thank V. K. Mel'nikov for the discussion of this work.

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Nesterenko, V.V. On the Lax representation for the nonlinear evolution equations. Czech J Phys 32, 668–671 (1982). https://doi.org/10.1007/BF01596714

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  • DOI: https://doi.org/10.1007/BF01596714

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