Shock waves and compactons for fifth-order nonlinear dispersion equaitons

2009/02/10 by В. А. Галактионов, V. A. Galaktionov, Galaktionov, V. A.
Mathematics · Physics and Astronomy · #35K55 #35K65 #Advanced Fiber Laser Technologies #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP #msc:35K55 #msc:35K65

paper · pdf · doi:10.48550/arxiv.0902.1632

38 pages, 17 figures

arxiv created 2009/02/10 · openalex publication_date 2009/02/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Fifth-order 1D nonlinear dispersion equations are shown to admit blow-up formation of shock waves as well as rarefaction waves. The concepts of smooth deformations are applied to distinguish "entropy" shocks from smooth rarefaction waves. Single point gradient catastrophe is shown to lead to nonuniqueness after blow-up.

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