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Abstract <p>Widespread interest in Sobolev-type equations has been observed since the second half of the 20th century. Sobolev-type equations can be used to describe a wide range of non-stationary processes in electromagnetic field theory, theory of plasma, etc. In this paper, we study one specific Sobolev-type equation, namely Oskolkov–Benjamin–Bona–Mahony–Burgers equation. The Painleve test is an effective tool for constructing general solutions to ODEs and PDEs. It allows 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 an ODE to find an important class of exact solutions of the Oskolkov–Benjamin–Bona–Mahony–Burgers equation.</p>

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Painleve Analysis of One Non-Classical Nonlinear Second Order Equation

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • A. I. Aristov

摘要

Abstract

Widespread interest in Sobolev-type equations has been observed since the second half of the 20th century. Sobolev-type equations can be used to describe a wide range of non-stationary processes in electromagnetic field theory, theory of plasma, etc. In this paper, we study one specific Sobolev-type equation, namely Oskolkov–Benjamin–Bona–Mahony–Burgers equation. The Painleve test is an effective tool for constructing general solutions to ODEs and PDEs. It allows 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 an ODE to find an important class of exact solutions of the Oskolkov–Benjamin–Bona–Mahony–Burgers equation.