Solitons pp 12-26 | Cite as

The Korteweg-de Vries Equation (KdV-Equation)

  • Gert Eilenberger
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 19)

Abstract

This is the classic example of an equation which exhibits solitons. Methods which are applicable to a large class of equations which exhibit solitons will be derived from the study of this equation and its properties, and we therefore devote a rather large part of this book to this topic.

Keywords

Soliton 

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References

  1. 2.1
    P.D. Lax: “Almost Periodic Solutions of the KdV Equation”, SIAM Review 18, 351–375 (1976). Particularly interesting for conservation laws. Section 2.3 is taken in part from here.CrossRefMATHMathSciNetGoogle Scholar
  2. 2.2
    R.M. Miura: “The Korteweg -deVries Equation: A Survey of Results”, SIAM Review 18, 412–479 (1976). Presents the exact results known for the KdV, especially the conservation laws. Easy to read, as it is quite detailed, and interesting from the historical point of view. 109 references (to 1975) on the KdV.CrossRefMATHADSMathSciNetGoogle Scholar
  3. 2.3
    L.J.F. Broer: “Hidden Hamiltonians of First order Equations, “Physica 79A, 583–596 (1975). A general investigation of how one can describe first-order equations, such as the KdV, by means of a Hamiltonian formalism. In sect. 2.2, we have simply taken the viewpoint of Saletan and Cromer (Theoretical Mechanics Ch. 9, John Wiley and Sons, New York 1971): namely, that a “Hamiltonian mechanics” is defined by the Lie algebra of the Poisson brackets.ADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1981

Authors and Affiliations

  • Gert Eilenberger
    • 1
  1. 1.Institut für FestkörperforschungKernforschungsanlage Jülich GmbHJülich 1Fed. Rep. of Germany

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