Cauchy problem for a nonstrictly hyperbolic equation on a half-plane with constant coefficients

We consider the Cauchy problem for a nonstrictly hyperbolic equation of arbitrary order with constant coefficients. The operator in the equation is a composition of first-order differential operators. The equation is supplemented with Initial conditions. We find the solution of this problem on a half-plane in analytic form in the case of two independent variables under some conditions on the coefficients.