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Conservation laws for classes of nonlinear evolution equations solvable by the spectral transform

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Abstract

The existence of conservation laws for novel classes of nonlinear evolution equations (with linearlyx-dependent coefficients) solvable by the spectral transform is investigated. A remarkably explicit representation is moreover obtained for the conserved quantities of the “old” classes of nonlinear evolution equations (withx-independent coefficients; including the Korteweg-de Vries equation, the modified Korteweg-de Vries equation, the nonlinear Schrödinger equation, etc.).

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Author notes

  1. F. Calogero & A. Degasperis

    Present address: Istituto di Fisica, Università di Roma, I-00185, Roma, Italy

Authors and Affiliations

  1. Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Italy

    F. Calogero & A. Degasperis

  2. International Centre for Theoretical Physics, I-34100, Trieste, Italy

    F. Calogero & A. Degasperis

Authors
  1. F. Calogero
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  2. A. Degasperis
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Communicated by J. Moser

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Calogero, F., Degasperis, A. Conservation laws for classes of nonlinear evolution equations solvable by the spectral transform. Commun.Math. Phys. 63, 155–176 (1978). https://doi.org/10.1007/BF01220850

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  • DOI: https://doi.org/10.1007/BF01220850

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