Laplace invariants for a generalized Boussinesq-Love equation


We construct Laplace invariants for an equation with a dominating fourth partial derivative. The determining equations are written out in terms of the Laplace invariants. We single out classes of equations admitting four-dimensional Lie algebras.

This is a preview of subscription content, access via your institution.


  1. 1.

    Ovsyannikov, L.V., Gruppovoi analiz differentsial’nykh uravnenii (Group Analysis of Differential Equations), Moscow: Nauka, 1978.

    Google Scholar 

  2. 2.

    Ibragimov, N.Kh., Group Analysis of Ordinary Differential Equations and the Invariance Principle in Mathematical Physics, Uspekhi Mat. Nauk, 1992, vol. 47, no. 4, pp. 83–144.

    MATH  MathSciNet  Google Scholar 

  3. 3.

    Tricomi, F., Lezioni sulle equazioni a derivate parziali, Turin, 1954. Translated under the title Lektsii po uravneniyam v chastnykh proizvodnykh, Moscow: Inostrannaya literatura, 1957.

    MATH  Google Scholar 

  4. 4.

    Ovsyannikov, L.V., Group Properties of Chaplygin Equations, Zh. Prikl. Mekh. Tekhn. Fiz., 1960, no. 3, pp. 126–145.

    Google Scholar 

  5. 5.

    Smirnov, V.I., Kurs vysshei matematiki (A Course of Higher Mathematics), Moscow: Nauka, 1974, vol. 1.

    Google Scholar 

  6. 6.

    Soldatov, A.P. and Shkhanukov, M.Kh., Boundary Value Problems with A. A. Samarskii’s General Nonlocal Condition for Higher-Order Pseudoparabolic Equations, Dokl. Akad. Nauk SSSR, 1987, vol. 297, no. 3, pp. 547–552.

    MathSciNet  Google Scholar 

  7. 7.

    Utkina, E.A., On a Fourth-Order Partial Differential Equation, Deposited in VINITI, Moscow, 1999, no. 2059-V99.

    Google Scholar 

  8. 8.

    Mironov, A.N., On the Riemann Method for Solving the Cauchy Problem, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 2, pp. 34–44.

    Google Scholar 

  9. 9.

    Dzhokhadze, O.M., On Laplace Invariants for Some Classes of Linear Partial Differential Equations, Differ. Uravn., 2004, vol. 40, no. 1, pp. 58–68.

    MathSciNet  Google Scholar 

  10. 10.

    Mironov, A.N., On the Laplace Invariants of a Fourth-Order Equation, Differ. Uravn., 2009, vol. 45, no. 8, pp. 1144–1149.

    MathSciNet  Google Scholar 

  11. 11.

    Utkina, E.A., On an Application of the Cascade Integration Method, Differ. Uravn., 2007, vol. 43, no. 4, pp. 566–569.

    MathSciNet  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to L. B. Mironova.

Additional information

Original Russian Text © A.N. Mironov, L.B. Mironova, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 1, pp. 131–135.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Mironov, A.N., Mironova, L.B. Laplace invariants for a generalized Boussinesq-Love equation. Diff Equat 51, 132–137 (2015).

Download citation


  • Maximal Dimension
  • Liouville Equation
  • Determine Equation
  • Longitudinal Wave
  • Love Equation