Differential Operators Defining Solutions to Iterated Hyperbolic-Type Equations

Hyperbolic-type differential equations and their iterations are widely used to solve problems related to vibration phenomena and other problems of mechanics and mathematical physics. The methods of solving such equations are the creation of differential and integral operators. In the article, differential operators are constructed that translate arbitrary functions into regular solutions of a hyperbolic equation of the second and higher orders. The Riquier problem for the hyperbolic equation of the fourth order is solved.