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- Alexander I. Bobenko, Wolfgang K. Schief
- Experimental Mathematics
- 1999

It is established that there exists an intimate connection between isometric deformations of polyhedral surfaces and discrete integrable systems. In particular, Sauer’s kinematic approach is adopted to show that second-order infinitesimal isometric deformations of discrete surfaces composed of planar quadrilaterals (discrete conjugate nets) are determined… (More)

A remarkable connection between soliton theory and an important and beautiful branch of the theory of graphical statics developed by Maxwell and his contemporaries is revealed. Thus, it is demonstrated that reciprocal triangles which constitute the simplest pair of reciprocal figures representing both a framework and a self-stress encapsulate the integrable… (More)

It is shown that the integrable discrete Schwarzian KP (dSKP) equation which constitutes an algebraic superposition formula associated with, for instance, the Schwarzian KP hierarchy, the classical Darboux transformation and quasi-conformal mappings encapsulates nothing but a fundamental theorem of ancient Greek geometry. Thus, it is demonstrated that the… (More)

The conformal geometry of the Schwarzian Davey-Stewartson II hierarchy and its discrete analogue is investigated. Connections with discrete and continuous isothermic surfaces and generalised Clifford configurations are recorded. An interpretation of the Schwarzian Davey-Stewartson II flows as integrable deformations of conformally immersed surfaces is given.

- Charles W McMonnies, Wolfgang K Schief
- Eye & contact lens
- 2006

PURPOSE
To examine the hypotheses that a "pushed" biomechanically coupled intrafibrillar transfer of curvature may be involved in corneal warpage (pseudo cone) development, which is observed with superior cornea-bearing rigid contact lens fittings, and that a "pulled" biomechanically coupled intrafibrillar transfer of curvature may be involved in… (More)

- W K Schief
- 2001

A novel class of discrete integrable surfaces is recorded. This class of discrete O surfaces is shown to include discrete analogues of classical surfaces such as isothermic, ‘linear’ Weingarten, Guichard and Petot surfaces. Moreover, natural discrete analogues of the Gaußian and mean curvatures for surfaces parametrized in terms of curvature coordinates are… (More)

- R Conte, C Rogers, W K Schief
- 2007

A nonlinear coupled system descriptive of multi-ion electrodiffusion is investigated and all parameters for which the system admits a single-valued general solution are isolated. This is achieved via a method initiated by Painlevé with the application of a test due to Kowalevski and Gambier. The solutions can be obtained explicitly in terms of Painlevé… (More)

- W. K. SCHIEF, W. K. Schief
- 2000

It is shown that an integrable class of helicoidal surfaces in Euclidean space E3 is governed by the Painlevé V equation with four arbitrary parameters. A connection with sphere congruences is exploited to construct in a purely geometric manner an associated Bäcklund transformation.

- A. S. Fokas, Colin Rogers, Wolfgang K. Schief
- Appl. Math. Lett.
- 2005

It is established that a nonlinear model for the evolution of methacrylate in wood may be reduced via a reciprocal transformation to a moving boundary problem amenable to analytic treatment. Therein, the nonlinearity in the original problem is removed to the boundary. A recently developed method for the analysis of initial-boundary value problems is then… (More)