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Application of the Painleve Test to a Nonlinear Partial Differential Equation

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Abstract

Sobolev-type equations can describe non-stationary processes in a semiconductor, plasma, hydrodynamic phenomena, and others. Widespread interest in them has been observed since the second half of the 20th century. They contain terms with mixed derivatives with respect to time and high order spatial variables. In this paper, we study one Sobolev-type equation, which describes a non-stationary process in a semiconductor medium. The Painleve test is an effective tool for constructing general solutions to ODEs and PDEs. It allows one to construct a general solution of an equation in the form of a Laurent series or to prove that this is impossible. In this paper, we apply the Painleve test to find a solution to the problem. As a result, it was found that when a certain relation is satisfied for the parameters of the problem, the Painleve test is passed and the solution exists in the required one.

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REFERENCES

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Funding

The study was supported by the Russian Science Foundation grant no. 22-21-00449.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991, Moscow, Russia

    Anatoliy Aristov, Anna Kholomeeva & Evgeniy Moiseev

  2. Federal Research Center Computer Science and Control of the Russian Academy of Sciences, 119333, Moscow, Russia

    Anatoliy Aristov, Anna Kholomeeva & Evgeniy Moiseev

Authors
  1. Anatoliy Aristov
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  2. Anna Kholomeeva
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  3. Evgeniy Moiseev
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Corresponding author

Correspondence to Anna Kholomeeva.

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(Submitted by A. M. Elizarov)

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Aristov, A., Kholomeeva, A. & Moiseev, E. Application of the Painleve Test to a Nonlinear Partial Differential Equation. Lobachevskii J Math 43, 1791–1794 (2022). https://doi.org/10.1134/S1995080222100031

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  • DOI: https://doi.org/10.1134/S1995080222100031

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