On solutions of the first-order PDE with a multidimensional symmetric integral and their modelling

The deterministic analog of the multidimensional Stratonovich integral is constructed. Method of solution of a system of equations with a multidimensional symmetric integral is elaborated. The method of characteristics for solving the Cauchy problem for first-order partial differential equations with a multidimensional symmetric integral is developed. This method reduces solving the initial-value problem of the above equations to solving a system of equations with a multidimensional symmetric integral.