Third-order nonlinear dispersion PDEs: shocks, rarefaction, and blow-up waves

2009/02/02 by В. А. Галактионов, V. A. Galaktionov, Galaktionov, V. A. +3 · 5 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP #msc:35K55 #msc:35K65

paper · pdf · doi:10.48550/arxiv.0902.0253

32 pages, 12 figures

arxiv created 2009/02/02 · arxiv updated 2009/12/01

Abstract

Various shock and rarefaction-type similarity solutions of the third-order nonlinear dispersion equation in 1D are constructed. Blow-up of some solutions are proved by different techniques.

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• Nonlinear dispersion equations: smooth deformations, compactons, and extensions to higher orders
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• Very Singular Similarity Solutions and Hermitian Spectral Theory for Semilinear Odd-Order PDEs
• Variational approach to complicated similarity solutions pf higher-order nonlinear PDEs. I

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