The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables

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dc.contributor.authorFroehlich, S.
dc.date.accessioned2025-11-27T14:59:10Z
dc.date.issued2018
dc.description.abstractThis paper extends, to a class of systems of semi-linear hyperbolic second order PDEs in three variables, the geometric study of a single nonlinear hyperbolic PDE in the plane as presented in [Anderson I.M., Kamran N., Duke Math. J. 87 (1997), 265-319]. The constrained variational bi-complex is introduced and used to define form-valued conservation laws. A method for generating conservation laws from solutions to the adjoint of the linearized system associated with a system of PDEs is given. Finally, Darboux integrability for a system of three equations is discussed, and a method for generating infinitely many conservation laws for such systems is described.
dc.description.sponsorshipI would like to express my heartfelt gratitude to my Ph.D. advisor, Professor Niky Kamran, for his constant encouragement and guidance throughout the preparation of this paper. I would also like to thank Professor Mark Fels for the lectures he presented during the spring of 2012 at McGill University, which contributed greatly to my understanding of Cartan’s structural classification of involutive overdetermined systems of PDEs. And for bringing to my attention the example presented in Section 3.1, I thank Professor Peter Vassiliou. Finally, I thank the referees of this paper for their many thoughtful and helpful comments.
dc.identifier.citationThe Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables / S. Froehlich // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 36 назв. — англ.
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2018.096
dc.identifier.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 35L65; 35A30; 58A15
dc.identifier.otherarXiv: 1712.03068
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/209861
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleThe Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2018, том 14, випуск за цей рік