2006/07/27 by Virgil U. Pierce, V. U. Pierce, Fei Tian +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math.AP #nlin.SI
paper · pdf · doi:10.48550/arxiv.nlin/0607061
38 pages, 8 figures
arxiv created 2006/07/27 · openalex publication_date 2006/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Whitham equations for the fifth order KdV equation. The equations are neither strictly hyperbolic nor genuinely nonlinear. We are interested in the solution of the Whitham equations when the initial values are given by a step function. We classify the step like initial data into eight different types. We construct self-similar solutions for each type.