Differential-algebraic solutions of the heat equation

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Buchstaber, Victor M.; Netay, Elena Yu.;
  • Subject: Mathematical Physics | Mathematics - Dynamical Systems
    arxiv: Nonlinear Sciences::Exactly Solvable and Integrable Systems

In this work we introduce the notion of differential-algebraic ansatz for the heat equation and explicitly construct heat equation and Burgers equation solutions given a solution of a homogeneous non-linear ordinary differential equation of a special form. The ansatz fo... View more
  • References (6)

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    [3] E. Hopf, The partial di erential equation ut + uux = uxx, Comm. Pure Appl. Math., 3:3 (1950), 201{230.

    [4] H. Bateman, A. Erdelyi, Higher transcendental functions. Vol. 1, 1953.

    [5] D. Mumford, Tata Lectures on Theta I, II, Birkhauser, Boston-Basel-Stuttgart, 1983-1984.

    Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia. E-mail address: bunkova@mi.ras.ru (E.Yu.Netay), buchstab@mi.ras.ru (V.M.Buchstaber)

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