Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy
Abstract
We consider two-component integrable generalizations of the dispersionless two-dimensional Toda lattice (2DTL) hierarchy connected with non-Hamiltonian vector fields, similar to the Manakov-Santini hierarchy generalizing the dKP hierarchy. They form a one-parametric family connected by hodograph-type transformations. Generating equations and Lax-Sato equations are introduced, and a dressing scheme based on the vector nonlinear Riemann problem is formulated. The simplest two-component generalization of the dispersionless 2DTL equation is derived, and its differential reduction analogous to the Dunajski interpolating system is presented. A symmetric two-component generalization of the dispersionless elliptic 2DTL equation is also constructed.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- October 2010
- DOI:
- 10.1088/1751-8113/43/43/434008
- arXiv:
- arXiv:1003.0287
- Bibcode:
- 2010JPhA...43Q4008B
- Keywords:
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- Nonlinear Sciences - Exactly Solvable and Integrable Systems
- E-Print:
- 10 pages, the text of the talk at NEEDS 09. Notations clarified, references added