Classical Solution of the First Mixed Problem for the Telegraph Equation with a Nonlinear Potential

For the telegraph equation with a nonlinear potential given in the first quadrant, we consider a mixed problem in which the Cauchy conditions are specified on the spatial half-line and the Dirichlet condition is specified on the time half-line. The solution is constructed by the method of characteristics in an implicit analytical form as a solution of some integral equations. The solvability of these equations, as well as the dependence on the initial data and the smoothness of their solutions, is studied. For the problem in question, the uniqueness of the solution is proved and the conditions under which its classical solution exists are established.