On an inverse problem for a system of quazilinear equations in partial derivatives of the first order

A method of studying solubility of an inverse problem for the system of quasilinear differentialequations in partial derivatives of the first orderis offered. With the help of a nonlinear method ofchar-acteristics based on introduction of an additionalparameter, a Cauchy problem is reduced to study thesystem of non-linear integral equations. For solution the inverse problem the restored functions arefound from the system of Volterra non-linear integral equations of the first kind with the help of non-linear integral transformation.