Alfred Michel Grundland - On k-wave solutions of quasilinear systems of partial differential equations

ocnmp:11341 - Open Communications in Nonlinear Mathematical Physics, February 15, 2024, Special Issue in Memory of Decio Levi - https://doi.org/10.46298/ocnmp.11341
On k-wave solutions of quasilinear systems of partial differential equationsArticle

Authors: Alfred Michel Grundland

    In this paper, we establish a relation between two seemingly unrelated concepts for solving first-order hyperbolic quasilinear systems of partial differential equations in many dimensions. These concepts are based on a variant of the conditional symmetry method and on the generalized method of characteristics. We present the outline of recent results on multiple Riemann wave solutions of these systems. An auxiliary result concerning a modification of the Frobenius theorem for integration is used. We apply this result in order to show that the conditional symmetry method can deliver larger classes of multiple Riemann wave solutions, through a simpler procedure, than the one obtained from the generalized method of characteristics. We demonstrate that solutions can be interpreted physically as a superposition of k single waves. These theoretical considerations are illustrated by examples of hydrodynamic-type systems in (n+1) dimensions.


    Volume: Special Issue in Memory of Decio Levi
    Published on: February 15, 2024
    Accepted on: October 6, 2023
    Submitted on: May 21, 2023
    Keywords: Mathematics - Analysis of PDEs,Mathematical Physics,35A08

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