Note on the correspondence of solutions of some systems of equations

This paper considers hyperbolic systems of equations of a certain type that describe one-dimensional nonlinear waves propagating in the same way in both $x$ directions. Each system of this type can be set in correspondence to a hyperbolic system of equations with a halved order, constructed on the basis of the initial system of equations. The similarity of the solutions of this system of equations and the original one is studied.