Constructing a class of solutions for the Hamilton-Jacobi equation in field theory

Abstract

A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of boundary conditions of the field equations is provided. The paper also puts into evidence the intrinsic limits of the Hamilton-Jacobi method as an algorithm to determine families of solutions of the field equations, showing how the choice of the boundary data is often limited by compatibility conditions.

arXiv comment16 pages; submitted to J. Math. Phys

References in corpus (2)

• Covariant hamiltonian formalism for field theory: Hamilton-Jacobi equation on the space G
• Constructing solutions of Hamilton-Jacobi equations for 2 D fields with one component by means of Baecklund transformations

Cited by in corpus (3)

• Hamilton-Jacobi Theory in k-Symplectic Field Theories
• Hamilton-Jacobi theory in k-cosymplectic field theories
• Existence of solutions for Hamiltonian field theories by the Hamilton-Jacobi technique