Extensions of the symmetry algebra and Lax representations for the two-dimensional Euler equation

Abstract

We find the twisted extensions of the symmetry algebra of the 2D Euler equation in the vorticity form and use them to construct new Lax representation for this equation. Then we generalize this result by considering the transformation Lie--Rinehart algebras generated by finite-dimensional subalgebras of the symmetry algebra and derive a family of Lax representations for the Euler equation. The family depends on functional parameters and contains a non-removable spectral parameter.

arXiv commentarXiv admin note: text overlap with arXiv:2303.07411

References in corpus (13)

• Vortices, circumfluence, symmetry groups and Darboux transformations of the (2+1)-dimensional Euler equation
• The four-dimensional Martinez Alonso--Shabat equation: reductions and nonlocal symmetries
• Integrable dispersionless PDE in 4D, their symmetry pseudogroups and deformations
• Symmetries of Differential Equations via Cartan's Method of Equivalence
• On the Structure of Lie Pseudo-Groups
• Coverings over Lax integrable equations and their nonlocal symmetries
• Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation
• Deformations of infinite-dimensional Lie algebras, exotic cohomology, and integrable nonlinear partial differential equations
• Lax representations with non-removable parameters and integrable hierarchies of PDEs via exotic cohomology of symmetry algebras
• One method for constructing exact solutions of equations of two-dimensional hydrodynamics of an incompressible fluid
• On the Metric Independent Exotic Homology
• Integrable partial differential equations and Lie--Rinehart algebras
• On the algebra of nonlocal symmetries for the 4D Mart\'ınez Alonso-Shabat equation