Related papers: The sTB-B Hierarchy
It is shown that a new class of classical multicomponent super KdV equations is bi-superHamiltonian by extending the method for the verification of graded Jacobi identity. The multicomponent extension of super mKdV equations is obtained by…
We study Jacobi-Lie Hamiltonian systems admitting Vessiot-Guldberg Lie algebras of Hamiltonian vector fields related to Jacobi structures on real low-dimensional Jacobi-Lie groups. Also, we find some examples of Jacobi-Lie Hamiltonian…
An analysis of extension of Hamiltonian operators from lower order to higher order of matrix paves a way for constructing Hamiltonian pairs which may result in hereditary operators. Based on a specific choice of Hamiltonian operators of…
We study Euclidean Romans supergravity in six dimensions with a non-trivial Abelian R-symmetry gauge field. We show that supersymmetric solutions are in one-to-one correspondence with solutions to a set of differential constraints on an…
We present a new form of the multi-boson reduction of KP hierarchy with Lax operator written in terms of boson fields abelianizing the second Hamiltonian structure. This extends the classical Miura transformation and the Kupershmidt-Wilson…
We construct the tri-Hamiltonian structure of the two-dimensional Toda hierarchy using the R-matrix theory.
We derive a one-step extension of the well known Swanson oscillator that describes a specific type of pseudo-Hermitian quadratic Hamiltonian connected to an extended harmonic oscillator model. Our analysis is based on the use of the…
We rewrite various lattice Hamiltonian in condensed matter physics in terms of U(2/2) operators that we introduce. In this representation the symmetry structure of the models becomes clear. Especially, the Heisenberg, the supersymmetric t-J…
We consider a fully pseudo-bosonic Swanson model and we show how its Hamiltonian $H$ can be diagonalized. We also deduce the eigensystem of $H^\dagger$, using the general framework and results deduced in the context of pseudo-bosons. We…
This paper investigates Hamiltonian properties of the algebro-geometric discretization of KP hierarchy introduced in \cite{Gie1}. A Poisson bracket is introduced. The system is related to the periodic band matrix system of \cite{vM-M}. It…
We introduce an extended version of the Swanson model, defined on a two-dimensional non commutative space, which can be diagonalized exactly by making use of pseudo-bosonic operators. Its eigenvalues are explicitly computed and the…
We construct Darboux transformations for the super-symmetric KP hierarchies of Manin--Radul and Jacobian types. We also consider the binary Darboux transformation for the hierarchies. The iterations of both type of Darboux transformations…
In this paper a list of $R$-matrices on a certain coupled Lie algebra is obtained. With one of these $R$-matrices, we construct infinitely many bi-Hamiltonian structures for each of the two-component BKP and the Toda lattice hierarchies. We…
A bilinear formulation for the supersymmetric two-boson equation is derived. As applications, some solutions are calculated for it. We also construct a bilinear Backlund transformation.
We extend the well-known theoretical treatment of the spontaneous symmetry breaking (SSB) in two-component systems, combining linear coupling and self-attractive nonlinearity, to a system in which the linear coupling competes with repulsive…
We present a new method for constructing $D$-dimensional minimally superintegrable systems based on block coordinate separation of variables. We give two new families of superintegrable systems with $N$ ($N\leq D$) singular terms of the…
The general method of the supersymmetrization of the soliton equations with the odd (bi) hamiltonian structure is established. New version of the supersymmetric N=2,4 (Modified) Korteweg de Vries equation is given, as an example. The second…
A brief introduction to the topic of spontaneous symmetry breaking (SSB) in conservative and dissipative nonlinear systems with an underlying double-well-potential structure is given. The reason is a discussion of a recent observation of…
This paper is dedicated to provide the global solutions of algebro-geometric type for all the equations of a new commuting hierarchy containing the Hunter-Saxton (HS) equation. Our main tools include the zero curvature method to derive the…
We present a family of exactly solvable models at arbitrary filling in any dimensions which exhibit novel superconductivity with interband pairing. By the use of the hidden $SU(2)$ algebra the Hamiltonians were diagonalized explicitly. The…