Eikonal type equations for geometrical singularities of solutions in field theory

DOI10.1016/0393-0440(94)90008-6zbMath0819.58038OpenAlexW1969397501MaRDI QIDQ1337165

Fedele Lizzi, Giovanni Sparano, Giuseppe Marmo, Alexandre M. Vinogradov

Publication date: 5 September 1995

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(94)90008-6

zbMATH Keywords

singularitiesMaxwell equationsSchrödinger equationHamilton-Jacobi equationsDirac equationcharacteristic equationpartial differential equationsfield theoryeikonal equationsKlein-Gordongeometric solutions

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) PDEs in connection with quantum mechanics (35Q40) Geometric theory, characteristics, transformations in context of PDEs (35A30) Propagation of singularities; initial value problems on manifolds (58J47) Classical field theories (70Sxx)

Related Items (8)

Hamiltonian theory of constrained impulsive motion ⋮ From symmetries of partial differential equations towards secondary (``quantized) calculus ⋮ Some remarks on contact manifolds, Monge–Ampère equations and solution singularities ⋮ Characteristics, bicharacteristics and geometric singularities of solutions of PDEs ⋮ Symmetries and reduction Part II — Lagrangian and Hamilton–Jacobi picture ⋮ Covariant Jacobi brackets for test particles ⋮ Discontinuous trajectories of Lagrangian systems with singular hypersurface ⋮ Covariant reduction of classical Hamiltonian Field Theories: From D’Alembert to Klein–Gordon and Schrödinger

Cites Work

• Geometry of nonlinear differential equations
• Extensions of the Poisson bracket to differential forms and multi-vector fields
• From symmetries of partial differential equations towards secondary (``quantized) calculus
• Singularities of multivalued solutions of nonlinear differential equations, and nonlinear phenomena
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