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SIGMA, 2018, Volume 14, 096, 49 pages (Mi sigma1395)  

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

Sara Froehlich

Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC H3A 0B9 Canada

Abstract: 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 to 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.

Keywords: Laplace transform; conservation laws; Darboux integrable; variational bi-complex; hyperbolic second-order equations.

DOI: https://doi.org/10.3842/SIGMA.2018.096

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Full text: https://www.imath.kiev.ua/~sigma/2018/096/
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Bibliographic databases:

ArXiv: 1712.03068
MSC: 35L65; 35A30; 58A15
Received: December 11, 2017; in final form August 24, 2018; Published online September 9, 2018
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Citation: Sara Froehlich, “The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables”, SIGMA, 14 (2018), 096, 49 pp.

Citation in format AMSBIB
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\paper The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables
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\vol 14
\papernumber 096
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