Related papers: The multicomponent 2D Toda hierarchy: dispersionle…
Generalizing the graded commutator in superalgebras, we propose a new bracket operation on the space of graded operators with an involution. We study properties of this operation and show that the Lax representation of the two-dimensional…
The dispersionless KP hierarchy is considered from the point of view of the twistor formalism. A set of explicit additional symmetries is characterized and its action on the solutions of the twistor equations is studied. A method for…
We rederive dispersionless Hirota equations of the dispersionless Toda hierarchy from the method of kernel formula provided by Carroll and Kodama. We then apply the method to derive dispersionless Hirota equations of the extended…
We show that conformal maps of simply connected domains with an analytic boundary to a unit disk have an intimate relation to the dispersionless 2D Toda integrable hierarchy. The maps are determined by a particular solution to the hierarchy…
We derive the discrete linear systems associated to multi--matrix models, the corresponding discrete hierarchies and the appropriate coupling conditions. We also obtain the $W_{1+\infty}$ constraints on the partition function. We then apply…
Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…
The expression of the large $N$ Harish Chandra--Itzykson--Zuber (HCIZ) integral in terms of the moments of the two matrices is investigated using an auxiliary unitary two-matrix model, the associated biorthogonal polynomials and integrable…
The Riemann-Hilbert problems for multiple orthogonal polynomials of types I and II are used to derive string equations associated to pairs of Lax-Orlov operators. A method for determining the quasiclassical limit of string equations in the…
We propose a new integrable N=2 supersymmetric Toda lattice hierarchy which may be relevant for constructing a supersymmetric one-matrix model. We define its first two Hamiltonian structures, the recursion operator and Lax--pair…
We establish the equivalence of a 2D contour dynamics to the dispersionless limit of the integrable Toda hierarchy constrained by a string equation. Remarkably, the same hierarchy underlies 2D quantum gravity.
We define a dispersionless tau-symmetric bihamiltonian integrable hierarchy on the space of pairs of functions analytic inside/outside the unit circle with simple poles at $0$/$\infty$ respectively, which extends the dispersionless 2D Toda…
A higher dimensional analogue of the dispersionless KP hierarchy is introduced. In addition to the two-dimensional ``phase space'' variables $(k,x)$ of the dispersionless KP hierarchy, this hierarchy has extra spatial dimensions…
This paper is focused on geometric aspects of two particular types of finite-variable reductions in the dispersionless Toda hierarchy. The reductions are formulated in terms of "Landau-Ginzburg potentials" that play the role of reduced Lax…
In this paper, we continue the study of the Davey-Stewartson system which is one of the most important$(2+1)$ dimensional integrable models. As we showed in the previous paper, the dDS (dispersionless Davey-Stewartson) system arises from…
Bi-Hamiltonian structure and Lax pair formulation with the spectral parameter of the generalized fermionic Toda lattice hierarchy as well as its bosonic and fermionic symmetries for different (including periodic) boundary conditions are…
Analytic-bilinear approach for construction and study of integrable hierarchies is discussed. Generalized multicomponent KP and 2D Toda lattice hierarchies are considered. This approach allows to represent generalized hierarchies of…
We study the thermodynamic limit of random partition models for the instanton sum of 4D and 5D supersymmetric U(1) gauge theories deformed by some physical observables. The physical observables correspond to external potentials in the…
We revisit dispersionless version of the multicomponent KP hierarchy considered previously by Takasaki and Takebe. In contrast to their study, we do not fix any distinguished component treating all of them on equal footing. We obtain…
The dDS (dispersionless Davey-Stewartson) hierarchy is constructed by two eigenfunctions of a special vector field. This hierarchy consists the infinite symmetries of the dDS system. Further, this paper explores the tau function, the…
New reductions of the 2D Toda equations associated with low-triangular difference operators are proposed. Their explicit Hamiltonian description is obtained.