Related papers: The Supersymmetric Two Boson Hierarchy
The topological classifications of quadratic bosonic systems according to the symmetries of the dynamic matrices from the equations of motion of closed systems and the effective Hamiltonians from the Lindblad equations of open systems are…
We obtain the bi-Hamiltonian structure of the super KP hierarchy based on the even super KP operator $\Lambda = \theta^{2} + \sum^{\infty}_{i=-2}U_{i} \theta^{-i-1}$, as a supersymmetric extension of the ordinary KP bi-Hamiltonian…
We introduce a new unified two-parameter $\{(\epsilon_x, \epsilon_t)\,|\epsilon_{x,t}=\pm1\}$ wave model (simply called ${\mathcal Q}_{\epsilon_x,\epsilon_t}^{(n)}$ model), connecting integrable local and nonlocal vector nonlinear…
N=2 supersymmetric extensions of both the periodic and non-periodic relativistic Toda lattice are built within the framework of the Hamiltonian formalism. A geodesic description in terms of a non-metric connection is discussed.
We consider the inhomogeneous biharmonic nonlinear Schr\"odinger equation $$ i u_t +\Delta^2 u+\lambda|x|^{-b}|u|^\alpha u = 0, $$ where $\lambda=\pm 1$ and $\alpha$, $b>0$. In the subctritical case, we improve the global well-posedness…
Using the lax pair, nonlocal symmetry of the coupled Hirota equation is obtained. By introducing an appropriate auxiliary dependent variable the nonlocal symmetry is successfully localized to a Lie point symmetry. For the closed…
The super-algebraic structure of a generalized version of the Jaynes-Cummings model is investigated. We find that a Z2 graded extension of the so(2,1) Lie algebra is the underlying symmetry of this model. It is isomorphic to the…
We investigate the bi-Hamiltonian structures associated with constrained dispersionless modified KP hierarchies which are constructed from truncations of the Lax operator of the dispersionless modified KP hierarchy. After transforming their…
We study the classical version of supersymmetric $W$-algebras. Using the second Gelfand-Dickey Hamiltonian structure we work out in detail $W_2$ and $W_3$-algebras.
The non-holonomic deformations of non-local integrable systems belonging to the Nonlinear Schrodinger family are studied using the Bi-Hamiltonian formalism as well as the Lax pair method. The non-local equations are first obtained by…
We investigate $n$-component systems of conservation laws that possess third-order Hamiltonian structures of differential-geometric type. The classification of such systems is reduced to the projective classification of linear congruences…
A bi-Hamiltonian formulation is proposed for triangular systems resulted by perturbations around solutions, from which infinitely many symmetries and conserved functionals of triangular systems can be explicitly constructed, provided that…
Recently the authors and J.M. Kress presented a special function recurrence relation method to prove quantum superintegrability of an integrable 2D system that included explicit constructions of higher order symmetries and the structure…
We discuss a large class of coset constructions of the N=2 sl(n|n-1) affine superalgebra. We select admissible subalgebras, i.e. subalgebras that induce linear chiral/antichiral constraints on the coset supercurrents. We show that all the…
Bi-Hamiltonian structure and Lax pair formulation with the spectral parameter of the generalized fermionic Toda lattice hierarchy as well as its bosonic and fermionic symmetries for different (including periodic) boundary conditions are…
The geometry of N=1 supersymmetric double field theory is revisited in superspace. In order to maintain the constraints on the torsion tensor, the local tangent space group of O(D) x O(D) must be expanded to include a tower of higher…
The Poisson structure of a coupled system arising from a supersymmetric breaking of N=1 Super KdV equations is obtained. The supersymmetric breaking is implemented by introducing a Clifford algebra instead of a Grassmann algebra. The…
We investigate 2d $\mathcal{N}=(0,4)$ supersymmetric theories obtained from a topologically-twisted reduction of 4d $\mathcal{N}=2$ class $\mathcal{S}$ theories on a Riemann surface. This study addresses subtle aspects of central charges,…
The nonlinear supersymmetry of one-dimensional systems is investigated in the context of the quantum anomaly problem. Any classical supersymmetric system characterized by the nonlinear in the Hamiltonian superalgebra is symplectomorphic to…
We discuss 2d duality transformations in the classical AdS5 x S5 superstring and their effect on the integrable structure. T-duality along four directions in Poincare parametrization of AdS5 maps the bosonic part of the superstring action…