Blazhko L. Symmetry properties and exact solutions of nonlinear hyperbolic type equations

The object: quasilinear wave equations. The aim: classification of quasilinear wave equations invariant with respect to Poincare and conformal algebras and construction of invariant soliton type solutions for sine-Gordon equation. The methods: Lie method, conditional symmetries, iterative procedure for nonlocal solution generation. The novelty: Lie symmetries of quasilinear wave equations are classified and a method of iterative procedure for nonlocal solution generation is created. The results: Lie symmetries classification problem of the considered equations was solved, a chain of exact solutions of sine-Gordon equation was constructed, and conditional symmetry operators with corresponding solution classes for multidimensional wave sine-Gordon equation were found. The scope: mathematical physics, electrodynamics, geometry.