Conditions for the Transformation of a Diffusion Wave into a Traveling Wave within the System of Burgers-type Equations

We study the new effect of the transition from N-wave to traveling wave behavior of the solution to the system of two Burgers-type equations arising from the study of the Schumpeterian dynamics of innovations. We explain the conditions under which the soliton-like propagating traveling-wave captures the diffusion wave and forms another traveling-wave (shock wave in the inviscid case). A method for determining the exact value of the propagation speed of the emerging evolutionary dynamics is described.