Solution examples of the Cauchy problem for some variants of the Frankl system of elliptic type

The work contains examples of faithful analytic solutions of the Cauchy problem for some elliptic systems of the first order quasilinear partial differential equations. The solutions are presented in explicit forms and in initial variables.The method of an additional argument as basical one has allowed to establish the qualitative causes of an incorrectness of solutions and to define conditions of the classical solutions existing.