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

Sara Froehlich

Symmetry, integrability and geometry: methods and applications, Tome 14 (2018)

Résumé

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.

Détail

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

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