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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209861 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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.
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| ISSN: | 1815-0659 |