Lax representations with non-removable parameters and integrable hierarchies of PDEs via exotic cohomology of symmetry algebras

Abstract

This paper develops the technique of constructing Lax representations for PDEs via non-central extensions generated by non-triivial exotic 2-cocycles of their contact symmetry algebras. We show that the method is applicable to the Lax representations with non-removable spectral parameters. Also we demonstrate that natural extensions of the symmetry algebras produce the integrable hierarchies associated to their PDEs.

arXiv admin note: text overlap with arXiv:1812.03338

References in corpus (3)

• Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation
• A Two-Component Generalization of the Integrable rdDym Equation
• On the Metric Independent Exotic Homology