On nonlinear superposition of shock waves for the KdV-Burgers equation
Alexey Samokhin
TL;DR
This paper investigates how two shock waves for the KdV-Burgers equation combine into a single, more complex shock wave, using numerical and graphical methods to analyze the transformation process.
Contribution
It introduces a detailed study of nonlinear superposition of shock waves for the KdV-Burgers equation, including numerical modeling and visualization of their transformation.
Findings
Superposition of shock waves results in a complex yet predictable single shock.
Numerical simulations effectively demonstrate the transformation process.
The structure of the resulting shock wave can be characterized explicitly.
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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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Advanced Fiber Laser Technologies