Six-dimensional heavenly equation. Dressing scheme and the hierarchy. (English) Zbl 1404.37079
Summary: 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.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 53C07 | Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) |
| 70S15 | Yang-Mills and other gauge theories in mechanics of particles and systems |
Keywords:
dispersionless integrable equations; heavenly equations; self-dual Yang-Mills equations; hyper-Kähler hierarchies; Lax-Sato equationsReferences:
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