Linear Dispersive Shocks

2019/08/23 by David A. Smith, Smith, David, Thomas Trogdon +3
Mathematics · Physics and Astronomy · #35G16 #35Q53 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1908.08716

openalex publication_date 2019/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a linear dispersive partial differential equation which manifests a number of qualitative features of dispersive shocks, typically thought to occur only in nonlinear models. The model captures much of the short time phenomenon but deviates from the full nonlinear model in its long time behavior. Though we limit our present discussion to dispersive shocks occurring in the Korteweg-de Vries equation, our work extends readily to other higher order dispersive models too.

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