相关论文: Equivalence of Two Approaches to the mKdV Hierarch…
The purpose of this paper is to develop the negative order MKdV hierarchy and to present a new related integrable Neumann-like Hamiltonian flow from the view point of inverse recursion operator and constraint method. The whole MKdV…
We apply a recent result of Borichev-Golinskii-Kupin on the Blaschke-type conditions for zeros of analytic functions on the complex plane with a cut along the positive semi-axis to the problem of the eigenvalues distribution of the…
Local commuting charges in sigma-models with classical Lie groups as target manifolds are shown to be related to the conserved quantities appearing in the Drinfeld-Sokolov (generalized mKdV) hierarchies. Conversely, the Drinfeld-Sokolov…
Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-function of the solution defined via reduction of the Toda lattice…
In this note the Choquet type operators are introduced, in connection to Choquet's theory of integrability with respect to a not necessarily additive set function. Based on their properties, a quantitative estimate for the nonlinear…
The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the KdV hierarchy. The null curves…
In this paper we generalize the quantization procedure of Toda-mKdV hierarchies to the case of arbitrary affine (super)algebras. The quantum analogue of the monodromy matrix, related to the universal R-matrix with the lower Borel subalgebra…
We consider the bi-Hamiltonian representation of the two-component coupled KdV equations discovered by Drinfel'd and Sokolov and rediscovered by Sakovich and Foursov. Connection of this equation with the supersymmetric…
In this {\color{red}{paper}} we discuss about the $ap-$Henstock-Kurzweil integrable functions on a topological vector spaces. Basic results of $ap-$Henstock-Kurzweil integrable functions are discussed here. We discuss the equivalence of the…
Frobenius manifolds (solutions of WDVV equations) in canonical coordinates are determined by the system of Darboux-Egoroff equations. This system of partial differential equations appears as a specific subset of the $n$-component KP…
In a recent paper Dargis and Mathieu introduced integrodifferential odd flows for the supersymmetric KdV equation. These flows are obtained from the nonlocal conservation laws associated with the fourth root of its Lax operator. In this…
Bracket preserving gauge equivalence is established between several two-boson generated KP type of hierarchies. These KP hierarchies reduce under symplectic reduction (via Dirac constraints) to KdV, mKdV and Schwarzian KdV hierarchies.…
The Lax operator of the Gaudin type models is a 1-form on the classical level. In virtue of the quantization scheme proposed in [Talalaev04] (hep-th/0404153) it is natural to treat the quantum Lax operator as a connection; this connection…
We propose a generalization of a Drinfeld-Sokolov scheme of attaching integrable systems of PDEs to affine Kac-Moody algebras. With every affine Kac-Moody algebra $\gg$ and a parabolic subalgebra $\gp$, we associate two hierarchies of PDEs.…
We introduce two flow approaches to the Loewner--Nirenberg problem on comapct Riemannian manifolds $(M^n,g)$ with boundary and establish the convergence of the corresponding Cauchy--Dirichlet problems to the solution of the…
We have derived a new system of mKdV-type equations which can be related to the affine Lie algebra $A_{5}^{(2)}$. This system of partial differential equations is integrable via the inverse scattering method. It admits a Hamiltonian…
In their recent inspiring paper Mironov and Morozov claim a surprisingly simple expansion formula for the Kontsevich-Witten tau-function in terms of the Schur Q-functions. Here we provide a similar conjecture for the Br\'ezin-Gross-Witten…
The Drinfeld - Sokolov construction associates a hierarchy of bihamiltonian integrable systems with every untwisted affine Lie algebra. We compute the complete set of invariants of the related bihamiltonian structures with respect to the…
For systems of evolutionary partial differential equations the tau-structure is an important notion which originated from the deep relation between integrable systems and quantum field theories. We show that, under a certain non-degeneracy…
We summarise the chain of comparisons showing Hinich's derived Maurer-Cartan functor gives an equivalence between differential graded Lie algebras and derived Schlessinger functors on Artinian differential graded-commutative algebras. We…