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The Parametrically Extended Kardar–Parisi–Zhang Equation, Its Dark-Type Generalization, and Integrability

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Geometric Methods in Physics XXXIX (WGMP 2022)

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Abstract

A physical problem of existence of conservation laws for a parametrically dependent Kardar–Parisi–Zhang equation, describing a spin glass growth dynamics, was analyzed within the gradient-holonomic- and optimal-control-based algorithms. The finitely parametric functional extensions of the Kardar–Parisi–Zhang equation and related conservation laws are constructed. A relationship of the Kardar–Parisi–Zhang equation to a so-called dark -type class of integrable dynamical systems on functional manifolds with hidden symmetries is stated.

In memoriam of outstanding Polish mathematical physicist

Anatol Odzijewicz (⋆ 6.10.1947 – †18.04.2022)

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Acknowledgements

The sincere acknowledgement belongs in due course to the Department of Computer Science and Telecommunication of the Cracow University of Technology for a local research grant.

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Authors and Affiliations

  1. Department of Computer Science and Telecommunication, Cracow University of Technology, Krakow, Poland

    Anatolij K. Prykarpatski

  2. Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, Lviv, Ukraine

    Anatolij K. Prykarpatski

  3. Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, Lviv, Ukraine

    Petro Ya. Pukach & Myroslava I. Kopych

Authors
  1. Anatolij K. Prykarpatski
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  2. Petro Ya. Pukach
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  3. Myroslava I. Kopych
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Corresponding author

Correspondence to Anatolij K. Prykarpatski .

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Editors and Affiliations

  1. Departamento de Física, CINVESTAV, Ciudad de México, Mexico

    Piotr Kielanowski

  2. Faculty of Mathematics, University of Białystok, Białystok, Poland

    Alina Dobrogowska

  3. Departments of Mathematics, Physics, Learning & Teaching, Rutgers University, New Brunswick, NJ, USA

    Gerald A. Goldin

  4. Faculty of Mathematics, University of Białystok, Białystok, Poland

    Tomasz Goliński

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Prykarpatski, A.K., Pukach, P.Y., Kopych, M.I. (2023). The Parametrically Extended Kardar–Parisi–Zhang Equation, Its Dark-Type Generalization, and Integrability. In: Kielanowski, P., Dobrogowska, A., Goldin, G.A., Goliński, T. (eds) Geometric Methods in Physics XXXIX. WGMP 2022. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-30284-8_21

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