Related papers: Backlund transformations for difference Hirota equ…
A difference analogue of the logistic equation, which preserves integrability, is derived from Hirota's bilinear difference equation. The integrability of the map is shown to result from the large symmetry associated with the B\"acklund…
The exact solutions of the $D^{(1)}_3$ model (or the $so(6)$ quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator…
We present Backlund transformations (BTs) with parameter for certain classical integrable n-body systems, namely the many-body generalised Henon-Heiles, Garnier and Neumann systems. Our construction makes use of the fact that all these…
We review recent results on the Bethe Ansatz solutions for the eigenvalues of the transfer matrix of an integrable open XXZ quantum spin chain using functional relations which the transfer matrix obeys at roots of unity. First, we consider…
The permutability of two Backlund transformations is employed to construct a non linear superposition formula and to generate a class of solutions for the N=2 super sine-Gordon model.
The spectral transformation Lanczos method for the sparse symmetric definite generalized eigenvalue problem for matrices $A$ and $B$ is an iterative method that addresses the case of semidefinite or ill conditioned $B$ using a shifted and…
The boundary algebraic Bethe Ansatz for a supersymmetric nineteen vertex-model constructed from a three-dimensional representation of the twisted quantum affine Lie superalgebra $U_{q}[\mathrm{osp}(2|2)^{(2)}]$ is presented. The eigenvalues…
Using the Weiss method of truncated singular expansions, we construct an explicit Backlund transformation of the Drinfeld-Sokolov-Satsuma-Hirota system into itself. Then we find all the special solutions generated by this transformation…
The nested algebraic Bethe ansatz is presented for the anisotropic supersymmetric $U$ model maintaining quantum supersymmetry. The Bethe ansatz equations of the model are obtained on a one-dimensional closed lattice and an expression for…
We study integrable models solvable by the nested algebraic Bethe ansatz and possessing GL(3)-invariant R-matrix. We obtain determinant representations for form factors of off-diagonal entries of the monodromy matrix. These representations…
Based on the inhomogeneous T-Q relation constructed via the off-diagonal Bethe Ansatz, the Bethe-type eigenstates of the XXZ spin-1/2 chain with arbitrary boundary fields are constructed. It is found that by employing two sets of gauge…
We summarize the results of our recent work on B\"acklund transformations (BTs), particularly focusing on the relationship of BTs and infinitesimal symmetries. We present a BT for an associated Degasperis-Procesi (aDP) equation and its…
We generalise the fusion procedure for the $A_{\n-1}^{(1)}$ open spin chain ($\n>2$) and we show that the transfer matrix satisfies a crossing property. We use these results to solve the $A_{\n-1}^{(1)}$ open spin chain with $U_{q}…
The Backlund transformation for pseudospherical surfaces, which is equivalent to that of the sine-Gordon equation, can be restricted to give a transformation on space curves that preserves constant torsion. We study its effects on closed…
We present the exact solution of a family of two-spins models. The models are solved by the algebraic Bethe ansatz method using the $gl(2)$-invariant $R$-matrix and a multi-spins Lax operator. The interactions are by the Heisenberg spins…
Eigenvalue transformations, which include solving time-dependent differential equations as a special case, have a wide range of applications in scientific and engineering computation. While quantum algorithms for singular value…
We diagonalize the transfer matrix of a solvable vertex model constructed by combining the vector representation of U_q[Sl(n|m)] and its dual by means of the quantum inverse scattering framework. The algebraic Bethe ansatz solution consider…
We apply the nested algebraic Bethe ansatz method to solve the eigenvalue problem for the SU(4) extension of the Hubbard model. The Hamiltonian is equivalent to the SU(4) graded permutation operator. The graded Yang-Baxter equation and the…
The transfer matrix of the general integrable open XXZ quantum spin chain obeys certain functional relations at roots of unity. By exploiting these functional relations, we determine the Bethe Ansatz solution for the transfer matrix…
A short proof is given to the fact that the additional symmetries of the KP hierarchy defined by their action on pseudodifferential operators, according to Fuchssteiner-Chen-Lee-Lin-Orlov-Shulman, coincide with those defined by their action…