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Symmetries of the One-Dimensional Fokker–Planck–Kolmogorov Equation with a Nonlocal Quadratic Nonlinearity

  • ELEMENTARY PARTICLE PHYSICS AND FIELD THEORY
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Russian Physics Journal Aims and scope

The one-dimensional Fokker–Planck–Kolmogorov equation with a special type of nonlocal quadratic nonlinearity is represented as a consistent system of differential equations, including a dynamical system describing the evolution of the moments of the unknown function. Lie symmetries are found for the consistent system using methods of classical group analysis. An example of an invariant-group solution obtained with an additional integral constraint imposed on the system is considered.

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Authors and Affiliations

  1. National Research Tomsk State University, Tomsk, Russia

    A. V. Shapovalov

  2. National Research Tomsk Polytechnic University, Tomsk, Russia

    E. A. Levchenko, A. Yu. Trifonov & A. V. Shapovalov

Authors
  1. E. A. Levchenko
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  2. A. Yu. Trifonov
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  3. A. V. Shapovalov
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Correspondence to E. A. Levchenko.

Additional information

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 79–84, February, 2017.

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Levchenko, E.A., Trifonov, A.Y. & Shapovalov, A.V. Symmetries of the One-Dimensional Fokker–Planck–Kolmogorov Equation with a Nonlocal Quadratic Nonlinearity. Russ Phys J 60, 284–291 (2017). https://doi.org/10.1007/s11182-017-1073-z

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  • DOI: https://doi.org/10.1007/s11182-017-1073-z

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