2003/01/01 by Roberto Camassa · 3 citations
Physics and Astronomy · Engineering · Mathematics · #Nonlinear Waves and Solitons #Numerical methods in engineering #Numerical methods for differential equations #Integrable system #Mathematics #Shallow water equations #Initial value problem #Partial differential equation #Waves and shallow water #Mathematical analysis #Riemann problem #Class (philosophy) #Wave equation #Applied mathematics #Riemann hypothesis #Physics #Computer science
paper · doi:10.3934/dcdsb.2003.3.115
openalex publication_date 2003/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
The initial value problem for a completelyintegrable shallow water wave equation isanalyzed through its formulation interms of characteristics. The resultingintegro-differential equations give rise to finite dimensionalprojections onto a class of distributional solutions of theequation, equivalent to taking the Riemann sumapproximation of the integrals. These finite dimensionalprojections are then explicitly solved via a Gram-Schmidtorthogonalization procedure. A particle methodbased on these reductions is implemented to solve the wave equationnumerically.