Related papers: Orthosymplectic superoscillator Lax matrices
The graph of a real symplectic linear transformation is an R-Lagrangian subspace of a complex symplectic vector space. The restriction of the complex symplectic form is thus purely imaginary and may be expressed in terms of the generating…
In this work we develop a general procedure for constructing the recursion operators fro non-linear integrable equations admitting Lax representation. Svereal new examples are given. In particular we find the recursion operators for some…
In a previous article [N. Delice, F.W. Nijhoff and S. Yoo-Kong, J. Phys. A: Math. Theor. 48(3) (2015), 035206] a novel class of elliptic Lax pairs for integrable lattice equations was introduced. The present article proposes a…
Some new developments in constrained Lax integrable systems and their applications to physics are reviewed. After summarizing the tau function construction of the KP hierarchy and the basic concepts of the symmetry of nonlinear equations,…
We extend the matrix-resolvent method of computing logarithmic derivatives of tau-functions to the nonlinear Schr\"odinger (NLS) hierarchy. Based on this method we give a detailed proof of a theorem of Carlet, Dubrovin and Zhang regarding…
We present an algebraic structure that provides an interesting and novel link between supersymmetry and quantum integrability. This structure underlies two classes of models that are exactly solvable in 1-dimension and belong to the $1/r^2…
We present the trigonometric Lax matrix and classical r-matrix for the Kowalevski gyrostat on so(4) algebra by using the auxiliary matrix algebras so(3,2) or sp(4).
This communication records some observations made in the course of studying one-relator groups from the point of view of residual solvability. As a contribution to clas- sification efforts we single out some relator types that render the…
We study the differential structure of the set of real logarithms of a non-singular real matrix, under the assumption that the matrix is either semi-simple or orthogonal.
The main question we raise here is the following one: given a real orthogonal n by n matrix X, is it true that there exists a rational orthogonal matrix Y having the same zero-pattern? We conjecture that this is the case and prove it for…
Using the intertwining matrix of the IRF-Vertex correspondence we propose a determinant representation for the generating function of the commuting Hamiltonians of the double elliptic integrable system. More precisely, it is a ratio of the…
A new class of structured matrices is presented and a closed form formula for their determinant is established. This formula has strong connections with the one for Vandermonde matrices.
We show how the recently discovered solvable rational extensions of Harmonic Oscillator and Morse potentials can be constructed in a direct and systematic way, without the need of supersymmetry, shape invariance, Darboux-Crum and…
We construct a Lax pair for the $E^{(1)}_6 $ $q$-Painlev\'e system from first principles by employing the general theory of semi-classical orthogonal polynomial systems characterised by divided-difference operators on discrete, quadratic…
We perform a classification of third order integrable systems of evolution equations with respect to higher symmetries. Applying it, we consider polynomial systems that are 0-homogeneous under a suitable weighting of variables with main…
Orthosymplectic Lie superalgebras are fundamental symmetries in modern physics, such as massive supergravity. However, their representations are far from being thoroughly understood. In the present paper, we completely determine the…
The existence of bi-Hamiltonian structures for the rational Harmonic Oscillator (non-central harmonic oscillator with rational ratio of frequencies) is analyzed by making use of the geometric theory of symmetries. We prove that these…
A construction of multidimensional parametric Yang-Baxter maps is presented. The corresponding Lax matrices are the symplectic leaves of first degree matrix polynomials equipped with the Sklyanin bracket. These maps are symplectic with…
We study a generalisation of the set-theoretic Yang-Baxter equation and investigate the connection between its solutions and matrix refactorisation problems. We refer to such solutions as scalene Yang-Baxter maps. Moreover, we construct…
We provide a calculus of mates for functors to the $\infty$-category of $\infty$-categories and extend Lurie's unstraightening equivalences to show that (op)lax natural transformations correspond to maps of (co)cartesian fibrations that do…