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

Pseudosymmetries and differential substitutions

  • 46 Accesses

  • 12 Citations

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

Literature Cited

  1. 1.

    A. M. Vinogradov, I. S. Krasil'shchik, and V. V. Lychagin, Introduction to the Geometry of Nonlinear Differential Equations [in Russian], Nauka, Moscow (1986).

  2. 2.

    N. Kh. Ibragimov, Transformation Groups in Mathematical Physics [in Russian], Nauka, Moscow (1983).

  3. 3.

    S. I. Svinolupov, "Second-order evolution equations admitting symmetries," Usp. Mat. Nauk,40, No. 5, 263–264 (1985).

  4. 4.

    N. H. Ibragimov, "Sur l'équivalence des équations d'évolution, qui admettent une algèbre de Lie—Bäcklund infinie," C. R. Acad. Sci. Paris Ser. 1,293, 657–660 (1981).

  5. 5.

    G. Rosen, "Nonlinear heat conduction in solid H2," Phys. Rev. Ser. B,19, No. 4, 2398–2399 (1979).

  6. 6.

    S. I. Svinolupov, V. V. Sokolov, and R. I. Yamilov, "On Bäcklund transformations for integrable evolution equations," Dokl. Akad. Nauk SSSR,271, No. 4, 802–805 (1983).

  7. 7.

    A. V. Zhiber and A. B. Shabat, "A system of equations ut = p(u, v), vx = q(u, v) possessing symmetries," Dokl. Akad. Nauk SSSR,277, No. 1, 29–33 (1984).

  8. 8.

    V. V. Sokolov, "On the structure of the algebra of symmetries for a one-field evolution equation," Dokl. Akad. Nauk SSSR,294, No. 5, 1065–1069 (1987).

  9. 9.

    V. G. Drinfel'd, S. I. Svinolupov, and V. V. Sokolov, "Classification of evolution equations of order five admitting an infinite series of conservation laws," Dokl. Akad. Nauk UkrSSR, Ser. A, No. 10, 8–10 (1985).

Download references

Additional information

Bashkir Branch, Academy of Sciences of the USSR. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 22, No. 2, pp. 47–56, April–June, 1988.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Sokolov, V.V. Pseudosymmetries and differential substitutions. Funct Anal Its Appl 22, 121–129 (1988). https://doi.org/10.1007/BF01077602

Download citation


  • Functional Analysis
  • Differential Substitution