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    Research Article|February 01 1985

    An infinite hierarchy of conservation laws and nonlinear superposition principles for self‐dual Einstein spaces

    Charles P. Boyer;
    Charles P. Boyer
    Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mex́ico20, D. F., Mexico
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    Jerzy F. Plebański
    Jerzy F. Plebański
    Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mexico 20, D. F., Mexico and Centro de Investigación y Estudios Avanzados del IPN, México D. F. 14, Ap. Post. 14‐740, Mexico
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    Charles P. Boyer
    , 
    Jerzy F. Plebański
    Instituto de Investigaciones en Matemáticas Aplicadas y en Sistemas, Universidad Nacional Autónoma de México, Mex́ico20, D. F., Mexico
    J. Math. Phys. 26, 229–234 (1985)
    Article history
    Received:
    February 06 1984
    Accepted:
    June 28 1984
    Citation

    Charles P. Boyer,Jerzy F. Plebański; An infinite hierarchy of conservation laws and nonlinear superposition principles for self‐dual Einstein spaces.J. Math. Phys. 1 February 1985; 26 (2): 229–234.https://doi.org/10.1063/1.526652

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      Self‐dual Einstein spaces are shown to admit an infinite hierarchy of conservation laws, and this hierarchy is then used to derive a formal version of Penrose’s twistor construction. The set of formal holomorphic bundles of fiber dimension 2 over the Riemann sphereP1 is shown to form a formal infinite group which is used to derive nonlinear superposition principles. As an example of our methods a new self‐dual Einstein space is obtained as the result of a ‘‘collision’’ of complexpp‐waves ‘‘traveling in opposite directions.’’

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      1985
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      • Online ISSN 1089-7658
      • Print ISSN 0022-2488
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