Integrable partial differential equations and Lie-Rinehart algebras. (English) Zbl 1498.35017
Summary: We develop the method for constructing Lax representations of pdes via the twisted extensions of their algebras of contact symmetries by generalizing the construction to the Lie-Rinehart algebras. We present examples of application of the proposed technique.
MSC:
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
| 17B80 | Applications of Lie algebras and superalgebras to integrable systems |
| 35A27 | Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs |
| 35B06 | Symmetries, invariants, etc. in context of PDEs |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 58J70 | Invariance and symmetry properties for PDEs on manifolds |
Software:
JetsReferences:
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