Six-dimensional heavenly equation. Dressing scheme and the hierarchy

Abstract

We consider six-dimensional heavenly equation as a reduction in the framework of general six-dimensional linearly degenerate dispersionless hierarchy. We characterise the reduction in terms of wave functions, introduce generating relation, Lax-Sato equations and develop the dressing scheme for the reduced hierarchy. Using the dressing scheme, we construct a class of solutions for six-dimensional heavenly equation in terms of implicit functions.

10 pages

References in corpus (3)

• Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation
• Linearly degenerate hierarchies of quasiclassical SDYM type
• Deformations of infinite-dimensional Lie algebras, exotic cohomology, and integrable nonlinear partial differential equations

Cited by in corpus (5)

• Coupled Dispersionless and Generalized Heisenberg Ferromagnet Equations with Self-Consistent Sources: Geometry and Equivalence
• Integrability properties of symmetric 4+4-dimensional heavenly type equation
• Dispersionless Limits of Some Integrable Equations
• Dispersionless Limits of Integrable Generalized Heisenberg Ferromagnet Equations
• Dephasing-Induced Distribution of Entanglement in Tripartite Quantum Systems