2012/04/19 by Michael, Bialy · 1 citation
Mathematics · Physics and Astronomy · #35L65 #35L67 #70H06 #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35L65 #msc:35L67 #msc:70H06 #nlin.SI
paper · pdf · doi:10.48550/arxiv.1204.4397
arxiv created 2012/04/19 · openalex publication_date 2012/04/19 · arxiv updated 2012/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note we analyze smooth solutions of a p-system of the mixed type. Motivating example for this is a 2-components reduction of the Benney moments chain which appears to be connected to theory of integrable systems. We don't assume a-priory that the solutions in question are in the Hyperbolic region. Our main result states that the only smooth solutions of the system which are periodic in x are necessarily constants. As for initial value problem we prove that if the initial data is strictly hyperbolic and periodic in x then the solution can not extend to [t0;+∞) and shocks are necessarily created.