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arXiv · 1003.0287

Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy

L. V. Bogdanov
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Abstract

We consider two-component integrable generalizations of the dispersionless 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, a dressing scheme based on the vector nonlinear Riemann problem is formulated. The simplest two-component generalization of the dispersionless 2DTL equation is derived, 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.

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L. V. Bogdanov. 2010-03-01. Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy. https://doi.org/10.1088/1751-8113/43/43/434008

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