2005/11/18 by A. M. Grundland, A.M. Grundland, B. Huard · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Cauchy–Riemann equations #Computational Fluid Dynamics and Aerodynamics #Construct (python library) #Hyperbolic partial differential equation #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Riemann hypothesis #Riemann problem #Riemann surface #Riemann's differential equation #Symmetry (geometry) #Type (biology) #math-ph #math.MP
paper · pdf · doi:10.2991/jnmp.2006.13.3.6
30 pages
arxiv created 2005/11/18 · openalex publication_date 2006/01/01 · arxiv updated 2015/06/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
In this paper we employ a “direct method” to construct rank-k solutions, expressible in Riemann invariants, to hyperbolic system of first order quasilinear differential equations in many dimensions. The most important feature of our approach is the analysis of group invariance properties of these solutions and applying the conditional symmetry reduction technique to the initial equations. We discuss in detail the necessary and sufficient conditions for existence of these type of solutions. We demonstrate our approach through several examples of hydrodynamic type systems; new classes of solutions are obtained in a closed form.