Related papers: Hirota Quadratic Equations for the Extended Toda H…
The construction of Quasi-topological gravities in three-dimensions requires coupling a scalar field to the metric. As shown in arXiv:2104.10172, the resulting "Electromagnetic" Quasi-topological (EQT) theories admit charged black hole…
This paper is dedicated to provide theta function representations of algebro-geometric solutions and related crucial quantities for the two-component Hunter-Saxton (HS2) hierarchy through studying an algebro-geometric initial value problem.…
In the series of recent publications we have proposed a novel approach to the classification of integrable differential/difference equations in 3D based on the requirement that hydrodynamic reductions of the corresponding dispersionless…
Using Hirota's method, solitons are constructed for affine Toda field theories based on the simply-laced affine algebras. By considering automorphisms of the simply-laced Dynkin diagrams, solutions to the remaining algebras, twisted as well…
Some new developments in constrained Lax integrable systems and their applications to physics are reviewed. After summarizing the tau function construction of the KP hierarchy and the basic concepts of the symmetry of nonlinear equations,…
We study line operators in the two-dimensional sigma-model on PSl(n|n) using the current-current OPEs. We regularize and renormalize these line operators, and compute their fusion up to second order in perturbation theory. In particular we…
Okounkov's generating function of the double Hurwitz numbers of the Riemann sphere is a hypergeometric tau function of the 2D Toda hierarchy in the sense of Orlov and Scherbin. This tau function turns into a tau function of the lattice KP…
We introduce and investigate a family of tau-functions of the 2D Toda hierarchy, which is a natural generalization of the hypergeometric family associated with Hurwitz numbers. For this family we prove a skew Schur function expansion…
The spectral eta-invariant of a self-adjoint elliptic differential operator on a closed manifold is rigid, provided that the parity of the order is opposite to the parity of dimension of the manifold. The paper deals with the calculation of…
This paper is dedicated to provide theta function representation of algebro-geometric solutions and related crucial quantities for the Hunter-Saxton (HS) hierarchy through studying a algebro-geometric initial value problem. Our main tools…
The origin of the bosonic and fermionic solutions, constructed in [1,2,3], to the symmetry equations corresponding to the two-dimensional bosonic and N=(2|2) supersymmetric Toda lattices is established, and algebras of the corresponding…
Building on the mapping relations between analytic functions and periodic functions using the abstract operators $\cos(h\partial_x)$ and $\sin(h\partial_x)$, and by defining the Zeta and related functions including the Hurwitz Zeta function…
The sets of the integrable lattice equations, which generalize the Toda lattice, are considered. The hierarchies of the first integrals and infinitesimal symmetries are found. The properties of the multi-soliton solutions are discussed.
Bachmann, Takeyama and Tasaka introduced a $\mathbb{Q}$-linear map $\phi$, which we call the symmetrization map in this paper, on the harmonic algebra $\mathfrak{H}^1$. They calculated $\phi(w)$ explicitly for an element $w$ in…
We extend the matrix-resolvent method of computing logarithmic derivatives of tau-functions to the nonlinear Schr\"odinger (NLS) hierarchy. Based on this method we give a detailed proof of a theorem of Carlet, Dubrovin and Zhang regarding…
In this paper, we study nonlinear integrable equations with three independent variables of the following types: Toda-type lattices, semi-discrete lattices, and fully discrete Hirota-Miwa type models. It is shown that integrable equations of…
We develop a fractional version of Hirota's bilinear calculus that is built directly from the spectral (Fourier-multiplier) fractional derivative on $\mathbb{R}$. For $0<\alpha\le 1$ we define \[ D_{\xi}^{\alpha}f\cdot g :=…
Locality is analyzed for Toda field theories by noting novel chiral description in the conventional nonchiral formalism. It is shown that the canonicity of the interacting to free field mapping described by the classical solution is…
New deformed affine algebras A_{\hbar,\eta}(\hat{g}) are defined for any simply-laced classical Lie algebra g, which are generalizations of the algebra A_{\hbar,\eta}(\hat{sl_2}) recently proposed by Khoroshkin, Lebedev and Pakuliak (KLP).…
In this paper, we present an explicit formula that connects the Kontsevich-Witten tau-function and the Hodge tau-function by differential operators belonging to the $\hat{GL(\infty)}$ group. Indeed, we show that the two tau-functions can be…