2016•arXiv (Cornell University)Open access

On nonlinear superposition of shock waves for the KdV-Burgers equation

Alexey Samokhin

Abstract

Superposition of explicit (analytic) monotone non-increasing shock waves for the KdV-Burgers equation is studied, modelled numerically and graphically presented. Initial profile chosen as a sum of two such shock waves gradually transforms into a single shock wave of a somewhat complex yet predictable structure. This transformation is demonstrated in detail.

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Key concepts: Korteweg–de Vries equation, Superposition principle, Shock wave, Burgers' equation, Shock (circulatory), Transformation (genetics), Nonlinear system, Mathematics