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Abstract <p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年1月1日

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  • L. V. Egorov

摘要

Abstract

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.