Traveling-wave Solution to the Schumpeterian Dynamics with Heterogeneous Imitation

The article studies a Schumpeterian dynamics model describing the interaction of two types of agents with a heterogeneous imitation range. Far-sighted agents have an infinite imitation range and the short-sighted ones have a finite imitation range. The evolution of their complementary distributions is described by the system of coupled Burgers-type equations. The traveling-wave solution of this system is presented with the conditions of existence for both unilateral and mutual influence. In both cases the density of short-sighted agents is captured by the soliton-like propagating density of the far-sighted agents and forms the shock wave as an entropy solution to the inviscid Burgers-type equation. Numerical experiments confirm the results.