Integrable structure in discrete shell membrane theory

Integrable structure in discrete shell membrane theory.

We present natural discrete analogues of two integrable classes of shell membranes. By construction, these discrete shell membranes are in equilibrium with respect to suitably chosen internal stresses and external forces. The integrability of the underlying equilibrium equations is proved by relating the geometry of the discrete shell membranes to discrete O surface theory. We establish connect...

A Hierarchy of Discrete Integrable Equation and its Hamiltonian Structure

In this paper a new discrete isospectral problem is constructed, from which a new Lax integrable discrete equation is generated and obtain its hierarchy structure. The Hamiltonian structures for the hierarchy of the Lax integrable discrete equation is established by using the trace identity which was proposed by Tu.

Discrete Moving Frames and Discrete Integrable Systems

Group-based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. Here we describe what we call a discrete group-based moving frame, which is essentially a sequence of moving frames with overlapping domains. We demonstrate a small set of generators of the algebra of invariants, which...

Discrete Integrable Systems and Geometry

A Symplectic Structure for String Theory on Integrable Backgrounds

We define regularised Poisson brackets for the monodromy matrix of classical string theory on R × S 3. The ambiguities associated with Non-Ultra Locality are resolved using the symmetrisation prescription of Maillet. The resulting brackets lead to an infinite tower of Poisson-commuting conserved charges as expected in an integrable system. The brackets are also used to obtain the correct symple...