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.
- Publication:
-
Physics Letters A
- Pub Date:
- January 2019
- DOI:
- 10.1016/j.physleta.2018.09.037
- arXiv:
- arXiv:1806.01500
- Bibcode:
- 2019PhLA..383...10B
- Keywords:
-
- Dispersionless integrable equations;
- Heavenly equations;
- Self-dual Yang-Mills equations;
- Hyper-Kähler hierarchies;
- Lax-Sato equations;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- General Relativity and Quantum Cosmology;
- Mathematical Physics;
- 37K10;
- 37K15;
- 37K25;
- 35Q75
- E-Print:
- 10 pages