The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables
Differential Geometry
2018-09-11 v2
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
Cite
@article{arxiv.1712.03068,
title = {The Variational Bi-Complex for Systems of Semi-Linear Hyperbolic PDEs in Three Variables},
author = {Sara Froehlich},
journal= {arXiv preprint arXiv:1712.03068},
year = {2018}
}