The one-dimensional Hubbard model is known to possess an extended su(2) symmetry and to be integrable. I introduce an integrable model with an extended su(n) symmetry. This model contains the usual su(2) Hubbard model and has a set of features that makes it the natural su(n) generalization of the Hubbard model. Complete integrability is shown by introducing the L-matrix and showing that the tra...

We investigate the integrable structure of spin chain models with centrally extended su(2|2) and psu(2, 2|4) symmetry. These chains have their origin in the planar AdS/CFT correspondence, but they also contain the one-dimensional Hubbard model as a special case. We begin with an overview of the representation theory of centrally extended su(2|2). These results are applied in the construction an...

Wewill discuss how to generate integrable couplings from zero curvature equations associated with matrix spectral problems. The key elements are matrix loop algebras consisting of block matrices with blocks of the same size or different sizes. Hamiltonian structures are furnished by applying the variational identity defined over semi-direct sums of Lie algebras. Illustrative examples include in...

We propose a new type of reduction for integrable systems of coupled matrix PDEs; this reduction equates one matrix variable with the transposition of another multiplied by an anti-symmetric constant matrix. Via this reduction, we obtain a new integrable system of coupled derivative mKdV equations and a new integrable variant of the massive Thirring model, in addition to already known systems. ...

we consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmpxypxypxy++++2(,)(,)(,)nnmnmyqxyqxyqxy++&=++. for where and are homogeneous polynomials of degree i. inside this class of polynomial differential equation we consider a subclass of darboux integrable systems. moreover, under additional conditions we proved such darboux integrable systems can have at most 1 limit cycle.

We consider a general class of boundary terms of the open XYZ spin-1/2 chain compatible with integrability. We have obtained the general elliptic solution of K-matrix obeying the boundary Yang-Baxter equation using the R-matrix of the eight vertex model and derived the associated integrable spin-chain Hamiltonian. 1+1 dimensional integrable models with boundaries find interesting applications i...

We investigate the integrable structures in an N = 2 superconformal Sp(N) Yang-Mills theory with matter, which is dual to an open+closed string system. We restrict ourselves to the BMN operators that correspond to free string states. In the closed string sector, an integrable structure is inherited from its parent theory, N = 4 SYM. For the open string sector, the planar one-loop mixing matrix ...