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A generalized variational algebra and conserved densities for linear evolution equations

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Abstract

The symbolic algebra of Gel'fand and Dikii is generalized to the case of n variables. Using this algebraic approach we give a rigorous characterization of the polynomial kernel of the variational derivative. This is applied to classify all the conservation laws for linear polynomial evolution equations of arbitrary order.

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References

  1. Gel'fandI.M. and DikiiL.A., Russian Math. Surveys 30:5, 77 (1975).

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  2. Galindo, A. and Martínez, L., to be published.

  3. Hodge, W.V. and Padoe, D., Methods of Algebraic Geometry, Cambridge Univ. Press, 1968.

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Authors and Affiliations

  1. Departamento de Física Teórica, Facultad de Ciencias Físicas, Ciudad Universitaria, Madrid-3, Spain

    L. Abellanas & A. Galindo

Authors
  1. L. Abellanas
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  2. A. Galindo
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Partially supported by the Junta de Energía Nuclear, Madrid.

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Abellanas, L., Galindo, A. A generalized variational algebra and conserved densities for linear evolution equations. Lett Math Phys 2, 399–404 (1978). https://doi.org/10.1007/BF00400166

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  • DOI: https://doi.org/10.1007/BF00400166

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