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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.
Received: December 11, 2017; in final form August 24, 2018; Published online September 9, 2018
Citation:
Sara Froehlich, “The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables”, SIGMA, 14 (2018), 096, 49 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1395 https://www.mathnet.ru/eng/sigma/v14/p96
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Statistics & downloads: |
Abstract page: | 255 | Full-text PDF : | 19 | References: | 18 |
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