Related papers: On the constrained KP hierarchy II, An additional …
An explanation for the so-called constrained hierarhies is presented by linking them with the symmetries of the KP hierarchy. While the existence of ordinary symmetries (belonging to the hierarchy) allows one to reduce the KP hierarchy to…
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.
We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar…
An analogue of the KP hierarchy, the SDiff(2) KP hierarchy, related to the group of area-preserving diffeomorphisms on a cylinder is proposed. An improved Lax formalism of the KP hierarchy is shown to give a prototype of this new hierarchy.…
Addendum to the paper Combinatorics of the Modular Group II The Kontsevich integrals, hep-th/9201001, by C. Itzykson and J.-B. Zuber (3 pages)
We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…
We give a unified description of our recent results on the the inter-relationship between the integrable infinite KP hierarchy, nonlinear $\hat{W}_{\infty}$ current algebra and conformal noncompact $SL(2,R)/U(1)$ coset model both at the…
We give some remarks on limit mixed Hodge structure and spectrum. These are more or less well-known to the specialists, and do not seem to be stated explicitly in the literature. However, they do not seem to be completely trivial to the…
In this paper we study the Hamiltonian structure of the second Painleve hierarchy, an infinite sequence of nonlinear ordinary differential equations containing PII as its simplest equation. The n-th element of the hierarchy is a non linear…
We propose a remarkably simple and explicit conjectural formula for a bihamiltonian structure of the double ramification hierarchy corresponding to an arbitrary homogeneous cohomological field theory. Various checks are presented to support…
Hamiltonian bifurcations in the context of noncanonical Hamiltonian matter models are described. First, a large class of 1 + 1 Hamiltonian multi-fluid models is considered. These models have linear dynamics with discrete spectra, when…
A small comment on the paper with the mentioned title by Carl M. Bender, Dorje C. Brody and Hugh F. Jones.
We show how to construct in an elementary way the invariant of the KHK discretisation of a cubic Hamiltonian system in two dimensions. That is, we show that this invariant is expressible as the product of the ratios of affine polynomials…
We consider the even parity superLax operator for the supersymmetric KP hierarchy of the form $L~=~D^2 + \sum_{i=0}^\infty u_{i-2} D^{-i+1}$ and obtain the two Hamiltonian structures following the standard method of Gelfand and Dikii. We…
This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredient of these developments has been the understanding of…
We introduce a generalisation of the KP hierarchy, closely related to the cyclic quiver and the Cherednik algebra $H_k(\mathbb Z_m)$. This hierarchy depends on $m$ parameters (one of which can be eliminated), with the usual KP hierarchy…
The string equation of type $(2,2g+1)$ may be thought of as a higher order analogue of the first Painlev\'e equation that corresponds to the case of $g = 1$. For $g > 1$, this equation is accompanied with a finite set of commuting…
One of the oldest methods for constructing integrable Hamiltonian systems, proposed by Jacobi, recently is being presented as a novel St\"{a}ckel lift construction related with Haantjes geometry. It may cause some confusion.
We study the conformal properties of the multi-constraint KP hierarchy and its nonstandard partner by covariantizing their corresponding Lax operators. The associated second Hamiltonian structures turn out to be nonlocal extension of $W_n$…
In this article, we treat G_2-geometry as a special case of multisymplectic geometry and make a number of remarks regarding Hamiltonian multivector fields and Hamiltonian differential forms on manifolds with an integrable G_2-structure; in…