Related papers: The Sigma Form for the PII Hierarchy

In this paper, we study Hamiltonian operators which are sum of a first order operator and of a Poisson tensor, in two spatial independent variables. In particular, a complete classification of these operators is presented in two and three…

Let (M,g) be an arbitrary pseudo-Riemannian manifold of dimension at least 3. We determine the form of all the conformal symmetries of the conformal (or Yamabe) Laplacian on (M,g), which are given by differential operators of second order.…

By using Lie symmetry methods, we identify a class of second order nonlinear ordinary differential equations invariant under at least one dimensional subgroup of the symmetry group of the Ermakov-Pinney equation. In this context, nonlinear…

In this paper we have performed second order normalization in the generalised photogravitaional restricted three body problem with Poynting-Robertson drag. We have performed Birkhoff's normalization of the Hamiltonian. For this we have…

We introduce integrable KdV type hierarchy associated naturally with arbitrary semi-simple Frobenius manifold. We present hierarchy in a Lax form and show that it admits bihamiltonian description.

Possible generalizations of the topological (or Berezinskii-Kosterlitz-Thouless) phase transition on multicomponent 2D systems with nontrivial vector homotopic group pi_1 are considered. Relations between Ginzburg-Landau like theories,…

In this paper, we present algebraic tools to obtain normal forms of $\omega$-Hamiltonian vector fields under a semisymplectic action of a Lie group, by taking into account the symmetries and reversing symmetries of the vector field. The…

This paper aims at the most comprehensive and systematic construction and tabulation of mechanical systems that admit a second invariant, quadratic in velocities, other than the Hamiltonian. The configuration space is in general a 2D…

We develop a new method for constructing integrable Hamiltonian hierarchies of Lax type equations, which combines the fractional powers technique of Gelfand and Dickey, and the classical Hamiltonian reduction technique of Drinfeld and…

The general method of the cojmplex supersymmetrization (supercomplexifications) of the soliton equations with the odd (bi) hamiltoninan structure is established. New version of the supercomplexified Kadomtsev-Petvishvili hierarchy is given.…

In this article we will obtain real and complex solutions to the Painleve IV equation through supersymmetric quantum mechanics. Then we will classify them into real solution hierarchies and also the complex solution hierarchies, which are…

The Li\'enard equation is used in various applications. Therefore, constructing general analytical solutions of this equation is an important problem. Here we study connections between the Li\'enard equation and some equations from the…

Using the curved bc-beta-gamma system (a tensor product of a Heisenberg and a Clifford vertex algebra) we introduce quantum analogy of Lichnerowicz differential. As follows we suggest new machinery for finding the Lichnerowicz-Poisson…

Gauge-invariant systems in unconstrained configuration and phase spaces, equivalent to second-class constraints systems upon a gauge-fixing, are discussed. A mathematical pendulum on an $n-1$-dimensional sphere $S^{n-1}$ as an example of a…

We solve the topological Poisson Sigma model for a Poisson-Lie group $G$ and its dual $G^*$. We show that the gauge symmetry for each model is given by its dual group that acts by dressing transformations on the target. The resolution of…

We study a 3-dimensional topological sigma-model, whose target space is a hyper-Kahler manifold X. A Feynman diagram calculation of its partition function demonstrates that it is a finite type invariant of 3-manifolds which is similar in…

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.…

This paper shows that the Ablowitz-Ladik hierarchy of equations (a well-known integrable discretization of the Non-linear Schrodinger system) can be explicitly viewed as a hierarchy of commuting flows which: (a) are Hamiltonian with respect…

Separate consideration of properties of roots of Third Painlev\'e transcendents (P_III-functions) is necessary due to irregularity the differential equation defining them reveals on the subset of the phase space where its solution would…

For a Hamiltonian system in R^{2n}, its two-system is defined in the phase space R^{2n} x sp(2n,R). In a sense, it is a combination of the original system and its system in variations with feedback. We study the Hamiltonian forms of the…