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arXiv · 1712.03068

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

Sara Froehlich
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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.

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Sara Froehlich. 2017-12-08. The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables. https://doi.org/10.3842/sigma.2018.096

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