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Old and new reductions of dispersionless Toda hierarchy
dispersionless Toda hierarchy finite-variable reduction waterbag model Landau-Ginzburg potential Lowner equations
2012/6/21
Two types of finite-variable reductions of the dispersionless Toda hierarchy are considered in the geometric perspectives. The reductions are formulated in terms of "Landau-Ginzburg potentials" that p...
The Algebro-Geometric Initial Value Problem for the Ruijsenaars-Toda Hierarchy and Quasi-Periodic Solutions
Ruijsenaars-Toda hierarchy complex-valued algebro-geometric solutions hyperelliptic curve Dubrovin-type equation Baker-Akhiezer vector
2012/4/27
We provide a detailed treatment of Ruijsenaars-Toda (RT) hierarchy with special emphasis on its the theta function representation of all algebro-geometric solutions. The basic tools involve hyperellip...
The $(N,M)$-bigraded Toda hierarchy is an extension of the original Toda lattice hierarchy. The pair of numbers $(N,M)$ represents the band structure of the Lax matrix which has $N$ upper and $M$ lowe...
The extended Toda hierarchy of Carlet, Dubrovin and Zhang is reconsidered in the light of a 2+1D extension of the 1D Toda hierarchy constructed by Ogawa. These two extensions of the 1D Toda hierarchy ...
The multicomponent 2D Toda hierarchy: generalized matrix orthogonal polynomials, multiple orthogonal polynomials and Riemann--Hilbert problems
multi-component 2D Toda hierarchy orthogonal polynomials Riemann--Hilbert problems
2010/4/7
We consider the relation of the multi-component 2D Toda hierarchy with matrix orthogonal and biorthogonal polynomials. The multi-graded Hankel reduction of this hierarchy is considered and the corresp...