Valentyn TYCHYNIN 1  and Olesya TERTYSHNYK 2
1Prydniprovs'ka State Academy of Civil Engineering and Architecture,
 24a Chernyshevsky Str.,
 49005 Dnipropetrovsk,
2Dnipropetrovsk National University,
 13 Naukovyi Provulok,
 49050 Dnipropetrovsk,

Classical and nonlocal symmetries of the equation
u11u22 - (u12)2 - (u00u22 - (u02)2) - (u11u00 - (u10)2) = 0

Lie classical symmetry of the equation u11u22 - (u12)2 - (u00u22 -( u02)2) - (u11u00 - (u10)2) = 0 is found and group-invariant solutions of it are constructed. The equation under investigation is linearized by the Legendre transformation. It allows us to obtain solutions of this equation via a nonlinear superposition principle.

  1. Fushchych W.I., Tychynin V.A., Generating solutions for nonlinear equations by the Legendre transformation, Proc. Acad. of Sci. Ukraine, 1992, N 7, p.20-25.