On the inverse problem for the quasilinear partial differential equation of the first order

A method of studying the solvability of the inverse problem for a quasilinear partial differential equation of first order is proposed. Using the nonlinear method of characteristics based on the introduction of an additional argument, the problem is reduced to the study of a nonlinear integral equation. The restored function is found from a nonlinear Volterra integral equation of the first kind by use of a nonlinear integral transformation.