Related papers: The Supersymmetric Two Boson Hierarchy
We provide the geometric actions for most general N=1 supergravity in two spacetime dimensions. Our construction implies an extension to arbitrary N. This provides a supersymmetrization of any generalized dilaton gravity theory or of any…
A large class of nonlocal equations and nonlocal charges for the Harry Dym hierarchy is exhibited. They are obtained from nonlocal Casimirs associated with its bi-Hamiltonian structure. The Lax representation for some of these equations is…
We show that a large class of non-degenerate second-order (maximally) superintegrable systems gives rise to Hessian structures, which admit natural (Hessian) coordinates adapted to the superintegrable system. In particular, abundant…
In this paper we study the problem of Hamiltonization of nonholonomic systems from a geometric point of view. We use gauge transformations by 2-forms (in the sense of Severa and Weinstein [29]) to construct different almost Poisson…
A nonlinear realization of super $W_{\infty}$ algebra is shown to exist through a consistent superLax formulation of super KP hierarchy. The reduction of the superLax operator gives rise to the Lax operators for $N=2$ generalized super KdV…
Supersymmetric extensions of the 1D and 2D Swanson models are investigated by applying the conformal bridge transformation (CBT) to the first order Berry-Keating Hamiltonian multiplied by $i$ and its conformally neutral enlargements. The…
We describe an $N=2$ supersymmetric Poisson vertex algebra structure of $N=1$ (resp. $N=0$) classical $W$-algebra associated with $\mathfrak{sl}(n+1|n)$ and the odd (resp. even) principal nilpotent element. This $N=2$ supersymmetric…
We show the existence of some new local, covariant and continuous symmetries for the BRST invariant Lagrangian density of a free two ($1 + 1$)-dimensional (2D) Abelian U(1) gauge theory in the framework of superfield formalism. The Noether…
We explicitly construct a supersymmetric $so(n)$ spin-Calogero model with an arbitrary even number $\cal N$ of supersymmetries. It features $\frac{1}{2}{\cal N}n(n{+}1)$ rather than ${\cal N}n$ fermionic coordinates and a very simple…
Three geometric formulations of the Hamiltonian structure of the macroscopic Maxwell equations are given: one in terms of the double de Rham complex, one in terms of L2 duality, and one utilizing an abstract notion of duality. The final of…
For the Harry Dym hierarchy, a non-standard Lax formulation is deduced from that of Korteweg-de Vries (KdV) equation through a reciprocal transformation. By supersymmetrizing this Lax operator, a new N=2 supersymmetric extension of the…
Nonlinear supersymmetry is characterized by supercharges to be higher order in bosonic momenta of a system, and thus has a nature of a hidden symmetry. We review some aspects of nonlinear supersymmetry and related to it exotic supersymmetry…
In this paper, we study supersymmetric or bi-superhamiltonian Euler equations related to the generalized Neveu-Schwarz algebra. As an application, we obtain several supersymmetric or bi-superhamiltonian generalizations of some well-known…
The canonical structure of classical non-linear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical non-linear sigma models known to be integrable, is shown to be governed by a fundamental…
The Lagrangian formalism for the N=2 supersymmetric sinh-Gordon model with a jump defect is considered. The modified conserved momentum and energy are constructed in terms of border functions. The supersymmetric Backlund transformation is…
Quantum superintegrable systems are solvable eigenvalue problems. Their solvability is due to symmetry, but the symmetry is often "hidden". The symmetry generators of 2nd order superintegrable systems in 2 dimensions close under commutation…
The supercomplexification is a special method of N=2 supersymmetrization of the integrable equations in which the bosonic sector could be reduced to the complex version of these equations. The N=2 supercomplex Korteweg de Vries,…
We demonstrate the common bihamiltonian nature of several integrable systems. The first one is an elliptic rotator that is an integrable Euler-Arnold top on the complex group GL(N) for any $N$, whose inertia ellipsiod is related to a choice…
The purpose of this work is to present some basic concepts about the non-linear sigma model in a simple and direct way. We start with showing the bosonic model and the Wess-Zumino-Witten term, making some comments about its topological…
The hierarchical nonlinear super-differential equations are identified which describe universal behavior of the discretized model of $2d$ supergravity recently proposed. This is done by first taking a double scaling limit of the super…