On some classes of fourth-order Bianchi equations with constant ratios of Laplace invariants

Abstract

On the basis of defining equations written out in terms of Laplace invariants, we single out some classes of fourth-order Bianchi equations similar to the well-known classes of hyperbolic equations with two independent variables admitting Lie algebras of maximum dimension.

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Correspondence to A. N. Mironov.

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Original Russian Text © A.N. Mironov, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 12, pp. 1572–1581.

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Mironov, A.N. On some classes of fourth-order Bianchi equations with constant ratios of Laplace invariants. Diff Equat 49, 1524–1533 (2013). https://doi.org/10.1134/S0012266113120070

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Keywords

  • Poisson Equation
  • Hyperbolic Equation
  • Maximum Dimension
  • Riemann Function
  • Laplace Invariant