Related papers: Lax structure and tau function for large BKP hiera…
We prove existence of the tau-function for the multi-component CKP hierarchy and find how it is related to the tau-function of the multi-component KP hierarchy.
It is quite basic in integrable systems to deriving Lax equations from bilinear equations. For multi--component KP theory, corresponding Lax structures are mainly constructed by matrix pseudo-differential operators for fixed discrete…
We introduce a class of reductions of the two-component KP hierarchy, which includes the Hirota-Ohta system hierarchy. The description of the reduced hierarchies is based on the Hirota bilinear identity and an extra bilinear relation…
Analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is discussed. It is based on the generalized Hirota identity. This approach allows to represent generalized hierarchies of…
We show that the multi-boson KP hierarchies possess a class of discrete symmetries linking them to the discrete Toda systems. These discrete symmetries are generated by the similarity transformation of the corresponding Lax operator. This…
Lattices of polynomial KP and BKP $\tau$-functions labelled by partitions, with the flow variables equated to finite power sums, as well as associated multipair KP and multipoint BKP correlation functions are expressed via generalizations…
The BKP hierarchy has a two-component analogue (the 2-BKP hierarchy). Dispersionless limit of this multi-component hierarchy is considered on the level of the $\tau$-function. The so called dispersionless Hirota equations are obtained from…
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 consider B\"acklund-Darboux transformations for integrable hierarchies of nonlinear equations such as KP, BKP and their close relatives referred to as modified KP and Schwarzian KP. We work in the framework of the bilinear formalism…
We construct generalized additional symmetries of a two-component BKP hierarchy defined by two pseudo-differential Lax operators. These additional symmetry flows form a Block type algebra with some modified(or additional) terms because of a…
We present a new form of the multi-boson reduction of KP hierarchy with Lax operator written in terms of boson fields abelianizing the second Hamiltonian structure. This extends the classical Miura transformation and the Kupershmidt-Wilson…
Restricting a linear system for the KP hierarchy to those independent variables t\_n with odd n, its compatibility (Zakharov-Shabat conditions) leads to the "odd KP hierarchy". The latter consists of pairs of equations for two dependent…
There are well-known constructions of integrable systems which are chains of infinitely many copies of the equations of the KP hierarchy ``glued'' together with some additional variables, e.g., the modified KP hierarchy. Another…
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…
The Toda hierarchy of size $N$ is well known to be analogous to the KdV hierarchy at $N$ goes to infinity. This paper shows that given $f$ a periodic function, there is a canonical way of defining the initial data for the Toda lattice…
We consider the Schwarzian KP and Harry Dym hierarchies in the framework of the bilinear formalism which is well known for such integrable hierarchies as KP, modified KP, BKP, Toda lattice and other. We show that, similarly to the bilinear…
By exhibiting the corresponding Lax pair representations we propose a wide class of integrable two-dimensional (2D) fermionic Toda lattice (TL) hierarchies which includes the 2D N=(2|2) and N=(0|2) supersymmetric TL hierarchies as…
In this paper, free Bosons are used to study some integrable properties of the CKP hierarchy, from the aspects of tau functions. Firstly, the modified CKP hierarchy is constructed by using free Bosons and the corresponding Lax structure is…
A generalized Toda Lattice equation is considered. The associated linear problem (Lax representation) is found. For simple case N=3 the $\tau$-function Hirota form is presented that allows to construct an exast solutions of the equations of…
We construct all polynomial tau-functions of the BKP, DKP and MDKP hierarches.