Nonlinear wave interactions for quasilinear hyperbolic 2x2 systems

Abstract

A reduction approach based upon the combined use of differential constraints theory and hodograph method is developed in order to determine closed form solutions for 2×2 hyperbolic quasilinear nonhomogeneous models. The problem of integrating the standard linear hodograph system associated with 2×2 homogeneous models is also considered. Along the lines of the proposed reduction approach different examples of 2×2 governing models are analyzed in order to highlight the flexibility of the provided solutions to describe hyperbolic wave processes.