caa a22 4500 606166076 CHVBK 20210128100656.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10440-014-9958-0 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9958-0 Multimode Solutions of First-Order Elliptic Quasilinear Systems [Elektronische Daten] [A. Grundland, V. Lamothe] Two new approaches to solving first-order quasilinear elliptic systems of PDEs in many dimensions are proposed. The first method is based on an analysis of multimode solutions expressible in terms of Riemann invariants, based on links between two techniques, that of the symmetry reduction method and of the generalized method of characteristics. Avariant of the conditional symmetry method for constructing this type of solution is proposed. Aspecific feature of that approach is an algebraic-geometric point of view, which allows the introduction of specific first-order side conditions consistent with the original system of PDEs, leading to a generalization of the Riemann invariant method for solving elliptic homogeneous systems of PDEs. Afurther generalization of the Riemann invariants method to the case of inhomogeneous systems, based on the introduction of specific rotation matrices, enables us to weaken the integrability condition. It allows us to establish a connection between the structure of the set of integral elements and the possibility of constructing specific classes of simple mode solutions. These theoretical considerations are illustrated by the examples of an ideal plastic flow in its elliptic region and a system describing a nonlinear interaction of waves and particles. Several new classes of solutions are obtained in explicit form, including the general integral for the latter system of equations. Springer Science+Business Media Dordrecht, 2014 Symmetry reduction method nationallicence Generalized method of characteristics nationallicence Riemann invariants nationallicence Multimode solutions nationallicence Grundland A. Centre de Recherche Mathématiques, Université de 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 138/1(2015-08-01), 81-113 0167-8019 138:1<81 2015 138 10440 https://doi.org/10.1007/s10440-014-9958-0 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/s10440-014-9958-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Grundland A. Centre de Recherche Mathématiques, Université de 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 138/1(2015-08-01), 81-113 0167-8019 138:1<81 2015 138 10440