A Geometric Framework to Compare PDEs and Classical Field Theories

DOI10.1007/978-3-031-25666-0_6arXiv1910.08614OpenAlexW4378881147MaRDI QIDQ6151332

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Publication date: 9 February 2024

Published in: Groups, Invariants, Integrals, and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1910.08614

zbMATH Keywords

jet space approach

Mathematics Subject Classification ID

Jets in global analysis (58A20) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Cites Work

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• Nonlocal trends in the geometry of differential equations: Symmetries, conservation laws, and Bäcklund transformations
• On the cohomology of the invariant Euler--Lagrange complex
• Gauge invariance and formal integrability of the Yang-Mills-Higgs equations
• Global Lie-Tresse theorem
• Local symmetries and conservation laws
• Nonlocal symmetries and the theory of coverings: An addendum to A. M. Vinogradov's 'Local Symmetries and Conservation Laws'
• Symmetry approaches for reductions of PDEs, differential constraints and Lagrange-Charpit method
• Multisymplectic Lagrangian and Hamiltonian formalisms of classical field theories
• Bäcklund transformations and their applications
• Invariant Euler--Lagrange equations and the invariant variational bicomplex
• Singularities in the geometric theory of differential equations
• Domains in infinite jet spaces: \({\mathcal C}\)-spectral sequences
• Existence theorems for analytic linear partial differential equations
• Integrability criteria for systems of nonlinear partial differential equations
• Characteristics, bicharacteristics and geometric singularities of solutions of PDEs
• GROUP FOLIATION OF DIFFERENTIAL EQUATIONS USING MOVING FRAMES
• Factorization of evolution equations
• Analogy between the Navier–Stokes equations and Maxwell’s equations: Application to turbulence