Integrable Boundary Conditions for Quad Equations, Open Boundary Reductions, and Integrable Mappings

Integrable boundary conditions and modified Lax equations

We consider integrable boundary conditions for both discrete and continuum classical integrable models. Local integrals of motion generated by the corresponding “transfer” matrices give rise to time evolution equations for the initial Lax operator. We systematically identify the modified Lax pairs for both discrete and continuum boundary integrable models, depending on the classical r-matrix an...

Asymmetric Integrable Quad-graph Equations

Integrable difference equations commonly have more low-order conservation laws than occur for non-integrable difference equations of similar complexity. We use this empirical observation to sift a large class of difference equations, in order to find candidates for integrability. It turns out that all such candidates have an equivalent affine form. These are tested by calculating their algebrai...

“New” boundary conditions in integrable lattice models

We consider the case of an integrable quantum spin chain with “soliton non-preserving” boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain framework. We construct the transfer matrix of the model, we study its symmetry and we find explicit expressions for its eigenvalues. Moreover, we derive a new set of Bethe ansatz equations by mean...

Integrable Boundary Conditions in Asymmetric Diffusion Processes

We study non-equilibrium reaction-diffusion processes with open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be determined in an elementary way. We give the equation which includes an auxiliary parameter and determines possible boundary conditions for the model to be solved exactly...

Integrable Field Theory with Boundary Conditions