Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Conditional invariance and exact solutions of the nonlinear equation

  • 22 Accesses

  • 17 Citations


The conditional invariance of the nonlinear heat equation is studied. Conditionalinvariance operators are applied for reducing the original equation to ordinary differential equations, and also for finding its exact solutions.

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    L. V. Ovsyannikov, “Group properties of the nonlinear heat equation,” Dokl. Akad. Nauk SSSR,125, 492–495 (1959).

  2. 2.

    V. A. Dorondnytsyn, I. V. Knyazeva, and S. R. Svishchevskii, “Group properties of the heat equation with a source in two-dimensional and three-dimensional cases,” Differents. Uravn.,19, No. 7, 1215–1224 (1983).

  3. 3.

    L. V. Ovsyannikov, Group analysis of Differential Equations, Academic Press, New York (1982).

  4. 4.

    V. I. Fushchich, V. M. Shtelen', and N. I. Serov, Symmetry Analysis and Exact Solutions of Nonlinear Equations of Mathematical Physics [in Russian], Naukova Dumka, Moscow (1989).

Download references

Author information

Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 10, pp. 1370–1376, October, 1990.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Serov, N.I. Conditional invariance and exact solutions of the nonlinear equation. Ukr Math J 42, 1216–1222 (1990). https://doi.org/10.1007/BF01057392

Download citation


  • Differential Equation
  • Exact Solution
  • Ordinary Differential Equation
  • Nonlinear Equation
  • Heat Equation