Related papers: Fully Supersymmetric Hierarchies From A Energy Dep…
In this talk, we describe our recent results on the supersymmetrization of the Harry Dym hierarchy as well as a newly constructed deformed Harry Dym hierarchy which is integrable with two arbitrary parameters. In various limits of these…
A study of Hamiltonian structures associated with supersymmetric Lax operators is presented. Following a constructive approach, the Hamiltonian structures of Inami-Kanno super KdV hierarchy and constrained modified super KP hierarchy are…
We review the results of several of our papers about the procedure of extension of Hamiltonians, allowing the construction of families of superintegrable systems with non-trivial polynomial first integrals (or symmetry operators) of…
An analysis of a $SU(2)_L \times SU(2)_R$ invariant, supersymmetric effective theory is given. The resulting leading and next to leading independent invariants are stated in terms of the underlying Killing vectors and K\"ahler potential.…
Of the two approaches to integrable systems associated to semisimple cohomological field theories (CohFTs), the one suggested by Dubrovin and Zhang and the more recent one using the geometry of the double ramification (DR) cycle, the second…
A new supersymmetric approach to the analysis of dynamical symmetries for matrix quantum systems is presented. Contrary to standard one dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy,…
In exactly solvable quantum-mechanical systems, ladder and intertwining operators play a central role because, if they are found, the energy spectra can be obtained algebraically. In this paper, we propose the spectral intertwining relation…
Degenerate tri-Hamiltonian structures of Shivamoggi and generalized Raychaudhuri equations are exhibited. For certain specific values of the parameters, it is shown that hyperchaotic L\"{u} and Qi systems are superintegrable and admit…
The supersymmetric completion of higher-derivative operators often requires introducing corrections to the scalar potential. In this paper we study these corrections systematically in the context of theories with $\mathcal{N}=1$ global and…
Given a hyperkahler manifold M, the hyperkahler structure defines a triple of symplectic structures on M; with these, a triple of Hamiltonians defines a so called hyperhamiltonian dynamical system on M. These systems are integrable when can…
We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian…
We discuss bi-Hamiltonian structures for integrable and superintegrable Hamiltonian system on the list of symplectic four-dimensional real Lie groups are classified by G. Ovando. In addition, we creat corresponding control matrix for…
The most general Dirac Hamiltonians in $(1+1)$ dimensions are revisited under the requirement to exhibit a supersymmetric structure. It is found that supersymmetry allows either for a scalar or a pseudo-scalar potential. Their spectral…
We discuss two distinct aspects in supersymmetric quantum mechanics. First, we introduce a new class of operators A and $\bar{A}$ in terms of anticommutators between the momentum operator and N+1 arbitrary superpotentials. We show that…
The N=2 supersymmetric {\alpha}=1 KdV hierarchy in N=2 superspace is considered and its rich symmetry structure is uncovered. New nonpolynomial and nonlocal, bosonic and fermionic symmetries and Hamiltonians, bi-Hamiltonian structure as…
Recently A.Galajinsky has suggested the N=1 supersymmetric extension of Euler top and made a few interesting observations on its properties [arXiv:2111.06083 [hep-th]]. In this paper we use the formulation of the Euler top as a system on…
The supersymmetric structure of a generalized non-Hermitian driven two-level system is demonstrated. A unitary rotation turns the Hamiltonian into a more convenient form. After decoupling a set of differential equations, the supersymmetric…
The Drinfeld-Sokolov construction of integrable hierarchies, as well as its generalizations, may be extended to the case of loop superalgebras. A sufficient condition on the algebraic data for the resulting hierarchy to be invariant under…
A simple construction of Whitham type hierarchies in all genera is suggested. Potentials of these hierarchies are written as integrals of hypergeometric type. Possible generalization for universal moduli space is also briefly discussed.
New supersymmetric partners of the modified Poschl-Teller and the Dirac's delta well potentials are constructed in closed form. The resulting one-parametric potentials are shown to be interrelated by a limiting process. The range of values…