Related papers: KP integrability of non-perturbative differentials
We consider the extended discrete KP hierarchy and show that similarity reduction of its subhierarchies lead to purely discrete equations with dependence on some number of parameters together with equations governing deformations with…
We begin the study of Khovanov-Lauda-Rouquier type algebras associated to moduli stacks of coherent sheaves on smooth projective curves. We consider the case of $\mathbb{P}^1$ and define, for any pair $(r,d)$ of a rank and a degree, the KLR…
We prove that simple, separable, monotracial UHF $L^{p}$-operator algebras are not classifiable up to (complete) isomorphism using countable structures, such as K-theoretic data, as invariants. The same assertion holds even if one only…
We find all formal solutions to the $\hbar$-dependent KP hierarchy. They are characterized by certain Cauchy-like data. The solutions are found in the form of formal series for the tau-function of the hierarchy and for its logarithm (the…
A few 2+1-dimensional equations belonging to the KP and modified KP hierarchies are shown to be sufficient to provide a unified picture of all the integrable cases of the cubic and quartic H\'enon-Heiles Hamiltonians.
The planar Kepler problem is complexified and we show that this holomorphic completely integrable Hamiltonian system has nontrivial monodromy.
We introduce the discrete hierarchy which naturally generalizes well known discrete KP hierarchy.
A systematic review of the various topologies that can be defined on the projective Hilbert space P(H), i.e., on the set of the pure quantum states, is presented. It is shown that P(H) carries a natural topology as well as a natural…
In this paper, we explore a notion of nonabelian Hodge structure on the fundamental group of an algebraic variety. This is approach is compared to some alternative approaches due to Morgan, Hain and others. We also give criteria for a…
Kricker constructed a knot invariant Z^{rat} valued in a space of Feynman diagrams with beads. When composed with the so called "hair" map H, it gives the Kontsevich integral of the knot. We introduce a new grading on diagrams with beads…
This paper concerns the explicit construction of extremal Kaehler metrics on total spaces of projective bundles, which have been studied in many places. We present a unified approach, motivated by the theory of hamiltonian 2-forms (as…
Two new families of completely integrable perturbations of the N-dimensional isotropic harmonic oscillator Hamiltonian are presented. Such perturbations depend on arbitrary functions and N free parameters and their integrals of motion are…
In this paper we deal with a stationary non-degenerate $p-$Kirchhoff type problem with critical non-linearity and a subcritical parametrized perturbation. We work on bounded domains of the Euclidean space, without any restriction on the…
We prove that a polynomial map is invertible if and only if some associated differential ring homomorphism is bijective. To this end, we use a theorem of Crespo and Hajto linking the invertibility of polynomial maps with Picard-Vessiot…
We prove that the generating function for the symmetric chromatic polynomial of all connected graphs satisfies (after appropriate scaling change of variables) the Kadomtsev--Petviashvili integrable hierarchy of mathematical physics.…
We completely describe Wahlquist-Estabrook prolongation structures (coverings) dependent on u, u_x, u_{xx}, u_{xxx} for the Krichever-Novikov equation u_t=u_{xxx}-3u_{xx}^2/(2u_x)+p(u)/u_x+au_x in the case when the polynomial…
In this paper, we consider a non-linear fourth-order evolution equation of Cahn-Hilliard-type on evolving surfaces with prescribed velocity, where the non-linear terms are only assumed to have locally Lipschitz derivatives. High-order…
A linear system, which generates a Moyal-deformed two-dimensional soliton equation as integrability condition, can be extended to a three-dimensional linear system, treating the deformation parameter as an additional coordinate. The…
We prove nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as $x\to\infty$. We find that the amplitude of the line soliton converges to that of the…
We continue the study of compact holomorphic $p$-contact manifolds $X$ that we introduced recently by expanding the discussion to include non-K\"ahler hyperbolicity issues and a differential calculus based on what we call the Lie derivative…