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A Kadomtsev–Petviashvili Hierarchy Driven by Equation Manifolds

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Abstract

The fact that (formally integrable) differential equations determine sub-bundles of appropriate infinite jet bundles allows us to introduce a ‘‘driven’’ Kadomtsev–Petviashvili (KP) hierarchy. We solve this hierarchy and we observe, as an application, that each solution to the KdV equation determines smooth solutions to our full KP hierarchy, and that these solutions are also smooth with respect to the ‘‘seed’’ (or initial) corresponding KdV solution.

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ACKNOWLEDGMENTS

V.R. thanks IHES for hospitality. V.R. considers this paper as a small tribute to A.M. Vinogradov and to his ‘‘Friday’s Physical Seminar’’ in MSU, and to V. Petviashvili and O. Pogutse who opened to mathematicians their spontaneous but so important computations later transformed into the Kadomtsev–Petviashvili and Kadomtsev–Pogutse equations.

Funding

The work of V.R. was partially supported by Russian Science Foundation (grant no. 23-41-00049), used for the presentation of the results in Sections 2–3 and in the Introduction. E.G.R.’s research is partially supported by the FONDECYT, grant no. 1201894.

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Authors and Affiliations

  1. Laboratoire Angevin de Recherche en Mathématiques, SFR MathSTIC, CNRS, Université d’Angers, F-49000, Angers, France

    J.-P. Magnot & V. Roubtsov

  2. Lycée Jeanne d’Arc, 63000, Clermont-Ferrand, France

    J.-P. Magnot

  3. Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile (USACH), Santiago, Chile

    E. G. Reyes

  4. Institute for Geometry and Physics, 34151, Trieste, Italy

    V. Roubtsov

  5. Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), 127051, Moscow, Russia

    V. Roubtsov

Authors
  1. J.-P. Magnot
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  2. E. G. Reyes
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  3. V. Roubtsov
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Correspondence to J.-P. Magnot, E. G. Reyes or V. Roubtsov.

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(Submitted by I. S. Krasil’shchik)

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Magnot, JP., Reyes, E.G. & Roubtsov, V. A Kadomtsev–Petviashvili Hierarchy Driven by Equation Manifolds. Lobachevskii J Math 44, 3963–3972 (2023). https://doi.org/10.1134/S1995080223090238

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