Linearly degenerate hierarchies of quasiclassical SDYM type
Abstract
We demonstrate that SDYM (self-dual Yang-Mills) equations for the Lie algebra of one-dimensional vector fields represent a natural reduction in the framework of a general linearly degenerate dispersionless hierarchy. We define the reduction in terms of wave functions and introduce a generating relation, Lax-Sato equations, and the dressing scheme for the reduced hierarchy. A multidimensional case is also discussed.
- Publication:
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Journal of Mathematical Physics
- Pub Date:
- September 2017
- DOI:
- 10.1063/1.5004258
- arXiv:
- arXiv:1603.00238
- Bibcode:
- 2017JMP....58i3505B
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics;
- Mathematics - Differential Geometry
- E-Print:
- 21 pages