Löwner equations and dispersionless hierarchies
arXiv:math/0605161 · doi:10.1088/0305-4470/39/37/010
Abstract
Using the Hirota representation of dispersionless dKP and dToda hierarchies, we show that the chordal Löwner equations and radial Löwner equations respectively serve as consistency conditions for one variable reductions of these integrable hierarchies. We also clarify the geometric meaning of this result by relating it to the eigenvalue distribution of normal random matrices in the large N limit.
30 pages, 5 figures, amsart.cls, graphics.sty, psfrag.sty etc. are used
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Cited by in corpus (11)
- Universal Whitham hierarchy, dispersionless Hirota equations and multi-component KP hierarchy
- Integrable (2+1)-dimensional systems of hydrodynamic type
- Growth processes related to the dispersionless Lax equations
- Dispersionless DKP hierarchy and elliptic Lowner equation
- Non-homogeneous systems of hydrodynamic type possessing Lax representations
- Loewner equations, Hirota equations and reductions of universal Whitham hierarchy
- Remarks on the waterbag model of dispersionless Toda Hierarchy
- Loewner evolution and finite dimensional reductions of integrable systems
- Multi-variable reductions of the dispersionless DKP hierarchy
- Loewner equations and reductions of dispersionless hierarchies
- Dispersionless version of the constrained Toda hierarchy and symmetric radial Löwner equation