Sixdimensional heavenly equation. Dressing scheme and the hierarchy
Abstract
We consider sixdimensional heavenly equation as a reduction in the framework of general sixdimensional linearly degenerate dispersionless hierarchy. We characterise the reduction in terms of wave functions, introduce generating relation, LaxSato equations and develop the dressing scheme for the reduced hierarchy. Using the dressing scheme, we construct a class of solutions for sixdimensional 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;
 Selfdual YangMills equations;
 HyperKähler hierarchies;
 LaxSato equations;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 General Relativity and Quantum Cosmology;
 Mathematical Physics;
 37K10;
 37K15;
 37K25;
 35Q75
 EPrint:
 10 pages