The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables
This 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 intr...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2018 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2018
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209861 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862538617462718464 |
|---|---|
| author | Froehlich, S. |
| author_facet | Froehlich, S. |
| citation_txt | The 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This 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.
|
| first_indexed | 2025-12-03T06:25:14Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209861 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-03T06:25:14Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Froehlich, S. 2025-11-27T14:59:10Z 2018 The 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. 1815-0659 2010 Mathematics Subject Classification: 35L65; 35A30; 58A15 arXiv: 1712.03068 https://nasplib.isofts.kiev.ua/handle/123456789/209861 https://doi.org/10.3842/SIGMA.2018.096 This 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. I 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables Article published earlier |
| spellingShingle | The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables Froehlich, S. |
| title | The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables |
| title_full | The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables |
| title_fullStr | The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables |
| title_full_unstemmed | The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables |
| title_short | The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables |
| title_sort | variational bi-complex for systems of semi-linear hyperbolic pdes in three variables |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209861 |
| work_keys_str_mv | AT froehlichs thevariationalbicomplexforsystemsofsemilinearhyperbolicpdesinthreevariables AT froehlichs variationalbicomplexforsystemsofsemilinearhyperbolicpdesinthreevariables |