caa a22 4500 60616619X CHVBK 20210128100657.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10440-014-9999-4 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9999-4 Solutions of First-Order Quasilinear Systems Expressed in Riemann Invariants [Elektronische Daten] [A. Grundland, V. Lamothe] We present a new technique for constructing solutions of quasilinear systems of first-order partial differential equations, in particular inhomogeneous ones. A generalization of the Riemann invariants method to the case of inhomogeneous hyperbolic and elliptic systems is formulated. The algebraization of these systems enables us to construct certain classes of solutions for which the matrix of derivatives of the unknown functions is expressible in terms of special orthogonal matrices. These solutions can be interpreted as nonlinear superpositions of k waves (or k modes) in the case of hyperbolic (or elliptic) systems, respectively. Theoretical considerations are illustrated by several examples of inhomogeneous hydrodynamic-type equations which allow us to construct solitonlike solutions (bumps and kinks) and multiwave (mode) solutions. Springer Science+Business Media Dordrecht, 2014 Generalized method of characteristics nationallicence Symmetry reduction method nationallicence Riemann invariants nationallicence Multiwave solutions nationallicence Multimode solutions nationallicence Grundland A. Centre de Recherches Mathématiques, Université du Montréal, Succc. Centre-ville, C.P. 6128, H3C 3J7, Montréal, QC, Canada aut Lamothe V. Département de Mathématiques et Statistique, Université de Montréal, Succc. Centre-ville, C.P. 6128, H3C 3J7, Montréal, QC, Canada aut Acta Applicandae Mathematicae Springer Netherlands 140/1(2015-12-01), 197-224 0167-8019 140:1<197 2015 140 10440 https://doi.org/10.1007/s10440-014-9999-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9999-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Grundland A. Centre de Recherches Mathématiques, Université du Montréal, Succc. Centre-ville, C.P. 6128, H3C 3J7, Montréal, QC, Canada aut NATIONALLICENCE 700 1- Lamothe V. Département de Mathématiques et Statistique, Université de Montréal, Succc. Centre-ville, C.P. 6128, H3C 3J7, Montréal, QC, Canada aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 140/1(2015-12-01), 197-224 0167-8019 140:1<197 2015 140 10440