Discontinuous traveling waves as weak solutions to the Fornberg-Whitham equation

2018/02/01 by Guenther Hoermann, Hoermann, Guenther
Mathematics · Physics and Astronomy · #35D30 #35L67 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP #msc:35D30 #msc:35L67

paper · pdf · doi:10.48550/arxiv.1802.00215

1 figure

openalex publication_date 2018/02/01 · arxiv created 2018/04/19 · arxiv updated 2018/04/23 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

We analyze the weak solution concept for the Fornberg-Whitham equation in case of traveling waves with a piecewise smooth profile function. The existence of discontinuous weak traveling wave solutions is shown by means of analysis of a corresponding planar dynamical system and appropriate patching of disconnected orbits.

Citations

• Wave breaking for nonlinear nonlocal shallow water equations

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