Conformal Maps and Integrable Hierarchies
Copyright policy )Conformal Maps and Integrable Hierarchies
Let \(D\) be simply connected domain in the complex \(z\)-plane bounded by a simple analytic curve \(\Gamma\). The authors show that conformal maps \(D\) onto unit disk \(G_1=\{x \mid|z|<1\}\) are given by a particular solution of the dispersionless 2D Toda hierarchy. They show that this solution obeys the string equation. Moreover they introduce a concept of the \(\tau\)-function for analytic curves.
- Kavli Institute for Theoretical Physics United States
- Joint Institute for Nuclear Research Russian Federation
- Landau Institute for Theoretical Physics Russian Federation
- University of Chicago United States
string equation, analytic curves, Geometric function theory, conformal maps, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), \(\tau\)-function, dispersionless 2D Toda hierarchy
string equation, analytic curves, Geometric function theory, conformal maps, Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.), \(\tau\)-function, dispersionless 2D Toda hierarchy
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