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  • 1. Broman, Göran
    et al.
    Rudenko, Oleg
    Submerged Landau jet: exact solutions, their meaning and application2010In: Physics Uspekhi, ISSN 1063-7869, E-ISSN 1468-4780, Vol. 53, no 1, p. 91-98Article, review/survey (Refereed)
    Abstract [en]

    Exact hydrodynamic solutions generalizing the Landau submerged jet solution are reviewed. It is shown how exact inviscid solutions can be obtained and how boundary layer viscosity can be included by introducing parabolic coordinates. The use of exact solutions in applied hydrodynamics and acoustics is discussed. A historical perspective on the discovery of a class of exact solutions and on the analysis of their physical meaning is presented.

  • 2. Rudenko, Oleg
    Giant nonlinearities in structurally inhomogeneous media and the fundamentals of nonlinear acoustic diagnostic techniques2006In: Physics Uspekhi, ISSN 1063-7869, E-ISSN 1468-4780, Vol. 49, no 1, p. 69-87Article, review/survey (Refereed)
  • 3.
    Rudenko, Oleg
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mechanical Engineering.
    Nonlinear dynamics of quadratically cubic systems2013In: Physics Uspekhi, ISSN 1063-7869, E-ISSN 1468-4780, Vol. 56, no 7, p. 683-690Article, review/survey (Refereed)
    Abstract [en]

    We propose a modified form of the well-known nonlinear dynamic equations with quadratic relations used to model a cubic nonlinearity. We show that such quadratically cubic equations sometimes allow exact solutions and sometimes make the original problem easier to analyze qualitatively. Occasionally, exact solutions provide a useful tool for studying new phenomena. Examples considered include nonlinear ordinary differential equations and Hopf, Burgers, Korteweg-de Vries, and nonlinear Schrodinger partial differential equations. Some problems are solved exactly in the space-time and spectral representations. Unsolved problems potentially solvable by the proposed approach are listed.

  • 4. Rudenko, Oleg
    Nonlinear Waves: some biomedical applications2007In: Physics Uspekhi, ISSN 1063-7869, E-ISSN 1468-4780, Vol. 50, no 4Article in journal (Refereed)
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