Nonlinear integro-differential equation with a high-degree hyperbolic operator

In this paper, we examine the solvability of the initial-value problem for a nonlinear integro-differential equation with a hyperbolic operator of arbitrary natural degree and a degenerate kernel. The expression of the high-order partial differential operator on the left-hand side of the equation through the superposition of first-order differential operators allowed us to represent the equation considered as an integral equation for unknown function along the characteristics. Also, we prove the unique solvability of the initial-value problem and the stability of solutions with respect to initial data.