By Professor Wolfgang Karl Schief

Books

Rogers CW; Schief WK, 2002, Backlund and Darboux Transformations, Cambridge University Press, UK

Book Chapters

Rogers C; Schief WK, 2025, 'Bäcklund and Darboux Transformations. Applications to Nonlinear Physical Systems', in Encyclopedia of Mathematical Physics, Elsevier, pp. 56 - 65, http://dx.doi.org/10.1016/b978-0-323-95703-8.00034-3

Schief WK; Rogers C, 2018, 'Ermakov-type systems in nonlinear physics and continuum mechanics', in Nonlinear Systems and Their Remarkable Mathematical Structures, CRC Press, pp. 541 - 541

Rogers C; Schief WK, 2018, 'On a novel resonant ermakov-nls system: Painlevé reduction', in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, pp. 1081 - 1098, http://dx.doi.org/10.1007/978-3-319-72456-0_49

Bobenko AI; Schief WK, 1999, 'Discrete indefinite affine spheres', in Discrete integrable geometry and physics, Oxford University Press, Oxford, UK, pp. 113 - 136

Schief WK; Rogers CW, 1996, 'On a Laplace sequence of nonlinear integrable Ernst-type equations', in Algebraic Aspects of Integrable Systems: In Memory of Irene Dorfman, in Progress in nonlinear Differential equations and their applications, Birkhauser Verlag, Boston, pp. 315 - 321

Oevel W; Schief W, 1993, 'Darboux Theorems and the KP Hierarchy', in Applications of Analytic and Geometric Methods to Nonlinear Differential Equations, Springer Netherlands, pp. 193 - 206, http://dx.doi.org/10.1007/978-94-011-2082-1_19

Journal articles

Schief WK; Hertrich-Jeromin U; Konopelchenko BG, 2025, 'Affine manifolds: The differential geometry of the multi-dimensionally consistent TED equation', Journal of Geometry and Physics, 207, http://dx.doi.org/10.1016/j.geomphys.2024.105366

Konopelchenko BG; Schief WK, 2024, 'Canonical reductions of the TED equation: integrable deformations of heavenly-type equations', Journal of Physics A: Mathematical and Theoretical, 57, http://dx.doi.org/10.1088/1751-8121/ad2e3d

Inoguchi JI; Jikumaru Y; Kajiwara K; Miura KT; Schief WK, 2023, 'Log-aesthetic curves: Similarity geometry, integrable discretization and variational principles[Formula presented]', Computer Aided Geometric Design, 105, http://dx.doi.org/10.1016/j.cagd.2023.102233

Rogers C; Schief WK, 2023, 'A two-dimensional magnetohydrodynamic system: geometric decomposition and canonical reduction', Meccanica, 58, pp. 1021 - 1029, http://dx.doi.org/10.1007/s11012-022-01579-5

Rogers C; Schief WK, 2023, 'Relativistic perfect fluids: integrability of the classical Taub system', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 479, pp. 20220645, http://dx.doi.org/10.1098/rspa.2022.0645

Demskoi DK; Rogers C; Schief WK, 2022, 'On 2+1-dimensional fibre-reinforced fluid motions: a magnetohydrodynamics nexus', Acta Mechanica, 233, pp. 4047 - 4062, http://dx.doi.org/10.1007/s00707-022-03303-6

Demskoi DK; Schief WK, 2021, 'On steady motions of an ideal fibre-reinforced fluid in a curved stratum. Geometry and integrability', Journal of Physics A: Mathematical and Theoretical, 54, pp. 505205, http://dx.doi.org/10.1088/1751-8121/ac38eb

Akopyan AV; Bobenko AI; Schief WK; Techter J, 2021, 'On Mutually Diagonal Nets on (Confocal) Quadrics and 3-Dimensional Webs', Discrete and Computational Geometry, 66, pp. 938 - 976, http://dx.doi.org/10.1007/s00454-020-00240-w

Konopelchenko BG; Schief WK; Szereszewski A, 2021, 'Self-dual Einstein spaces and the general heavenly equation. Eigenfunctions as coordinates', Classical and Quantum Gravity, 38, pp. 1 - 31, http://dx.doi.org/10.1088/1361-6382/abd145

Hoffmann T; Schief WK; Steinmeier J, 2021, 'On Discrete Conjugate Semi-Geodesic Nets', International Mathematics Research Notices, 2022, http://dx.doi.org/10.1093/imrn/rnaa394

Demskoi DK; Schief WK, 2020, 'On non-steady planar motions of fibre-reinforced fluids. Geometry and integrable structure', Journal of Physics A: Mathematical and Theoretical, 53, pp. 1 - 13, http://dx.doi.org/10.1088/1751-8121/abbec2

Rogers C; Schief WK; Malomed B, 2020, 'On modulated coupled systems. Canonical reduction via reciprocal transformations', Communications in Nonlinear Science and Numerical Simulation, 83, pp. 105091, http://dx.doi.org/10.1016/j.cnsns.2019.105091

Bobenko AI; Schief WK; Techter J, 2020, 'Checkerboard incircular nets: Laguerre geometry and parametrisation', Geometriae Dedicata, 204, pp. 97 - 129, http://dx.doi.org/10.1007/s10711-019-00449-x

Rogers C; Ruggeri T; Schief WK, 2020, 'On relativistic gasdynamics: Invariance under a class of reciprocal-type transformations and integrable Heisenberg spin connections: On relativistic gasdynamics', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 476, pp. 20200487, http://dx.doi.org/10.1098/rspa.2020.0487

Konopelchenko BG; Schief WK, 2019, 'On an integrable multi-dimensionally consistent 2n+2n-dimensional heavenly-type equation', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 475, pp. 20190091, http://dx.doi.org/10.1098/rspa.2019.0091

McCarthy A; Schief WK, 2018, 'Discrete projective minimal surfaces', Advances in Mathematics, 336, pp. 1 - 37, http://dx.doi.org/10.1016/j.aim.2018.07.027

Schief WK; Szereszewski A, 2018, 'Surface theory in discrete projective differential geometry. I. A canonical frame and an integrable discrete Demoulin system', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 474, pp. 20170770, http://dx.doi.org/10.1098/rspa.2017.0770

Inoguchi JI; Kajiwara K; Miura KT; Sato M; Schief WK; Shimizu Y, 2018, 'Log-aesthetic curves as similarity geometric analogue of Euler's elasticae', Computer Aided Geometric Design, 61, pp. 1 - 5, http://dx.doi.org/10.1016/j.cagd.2018.02.002

Bobenko AI; Schief WK; Suris YB; Techter J, 2018, 'On a Discretization of Confocal Quadrics. A Geometric Approach to General Parametrizations', International Mathematics Research Notices, 2020, pp. 10180 - 10230, http://dx.doi.org/10.1093/imrn/rny279

Hanke M; Penev S; Schief W; Weissensteiner A, 2017, 'Random orthogonal matrix simulation with exact means, covariances, and multivariate skewness', European Journal of Operational Research, 263, pp. 510 - 523, http://dx.doi.org/10.1016/j.ejor.2017.05.023

Schief WK, 2017, 'Gaussian and mean curvatures for discrete asymptotic nets', Journal of Geometry and Physics, 114, pp. 109 - 123, http://dx.doi.org/10.1016/j.geomphys.2016.11.031

McCarthy A; Schief WK, 2017, 'On the Combinatorics of Demoulin Transforms and (Discrete) Projective Minimal Surfaces', Discrete and Computational Geometry, 57, pp. 215 - 230, http://dx.doi.org/10.1007/s00454-016-9827-x

Rogers C; Schief WK, 2016, 'On Ermakov–Painlevé II systems. Integrable reduction', Meccanica, 51, pp. 2967 - 2974, http://dx.doi.org/10.1007/s11012-016-0546-4

Bobenko AI; Schief WK, 2016, 'Circle Complexes and the Discrete CKP Equation', International Mathematics Research Notices, 2017, pp. 1504 - 1561, http://dx.doi.org/10.1093/imrn/rnw021

Kodama Y; Konopelchenko B; Schief WK, 2015, 'Critical points, Lauricella functions and Whitham-type equations', Journal of Physics A: Mathematical and Theoretical, 48, http://dx.doi.org/10.1088/1751-8113/48/22/225202

Bobenko AI; Schief WK, 2015, 'Discrete line complexes and integrable evolution of minors', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471, pp. 20140819, http://dx.doi.org/10.1098/rspa.2014.0819

Schief W, 2015, 'Meistersterne in der FUßball-Bundesliga', Mitteilungen der Deutschen Mathematiker-Vereinigung, 23, http://dx.doi.org/10.1515/dmvm-2015-0032

King AD; Schief WK, 2015, 'Bianchi hypercubes and a geometric unification of the hirota and miwa equations', International Mathematics Research Notices, 2015, pp. 6842 - 6878, http://dx.doi.org/10.1093/imrn/rnu143

Huhnen-Venedey E; Schief WK, 2015, 'On weingarten transformations of hyperbolic nets', International Mathematics Research Notices, 2015, pp. 2021 - 2081, http://dx.doi.org/10.1093/imrn/rnt354

Bobenko AI; Schief WK; Suris YB; Techter J, 2015, 'On a discretization of confocal quadrics. I. An integrable systems approach', Journal of Integrable Systems, 1, pp. xyw005, http://dx.doi.org/10.1093/integr/xyw005

Konopelchenko BG; Schief WK, 2014, 'Integrable discretization of hodograph-type systems, hyperelliptic integrals and Whitham equations', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470, http://dx.doi.org/10.1098/rspa.2014.0514

Rogers C; Schief WK, 2014, 'The classical Korteweg capillarity system: Geometry and invariant transformations', Journal of Physics A: Mathematical and Theoretical, 47, http://dx.doi.org/10.1088/1751-8113/47/34/345201

Rogers C; Schief WK, 2014, 'On q-Gaussian Integrable Hamiltonian Reductions in Anisentropic Magneto-gasdynamics', Acta Applicandae Mathematicae, 132, pp. 515 - 525, http://dx.doi.org/10.1007/s10440-014-9926-8

Rogers C; Schief WK, 2014, 'On q-Gaussian Integrable Hamiltonian Reductions in Anisentropic Magneto-gasdynamics', Acta Applicandae Mathematicae, http://dx.doi.org/10.1007/s10440-014-9926-8

Schief WK, 2014, 'Integrable structure in discrete shell membrane theory', Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470, http://dx.doi.org/10.1098/rspa.2013.0757

Rogers C; Schief WK, 2014, 'On a boussinesq capillarity system: Hamiltonian reductions and associated quartic geometries', Studies in Applied Mathematics, 132, pp. 1 - 12, http://dx.doi.org/10.1111/sapm.12017

Schief WK; An H; Rogers C, 2013, 'Universal and integrable aspects of an elliptic vortex representation in 2+1-dimensional magneto-gasdynamics', Studies in Applied Mathematics, 130, pp. 49 - 79, http://dx.doi.org/10.1111/j.1467-9590.2012.00559.x

King AD; Schief WK, 2012, 'Clifford lattices and a conformal generalization of Desargues' theorem', Journal of Geometry and Physics, 62, pp. 1088 - 1096, http://dx.doi.org/10.1016/j.geomphys.2011.12.009

Rogers CW; Schief WK, 2012, 'Connection of an integrable inhomogeneous Heisenberg spin equation to a hydrodynamic-type system with collision term', JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 45, pp. Article number 432002, http://dx.doi.org/10.1088/1751-8113/45/43/432002

Schief WK; Rogers CW, 2012, 'The Euler Equations of Spatial Gasdynamics and the Integrable Heisenberg Spin Equation', Studies in Applied Mathematics, 128, pp. 407 - 419, http://dx.doi.org/10.1111/j.1467-9590.2011.00539.x

Rogers CW; Schief WK, 2011, 'On the integrability of a Hamiltonian reduction of a 2+1-dimensional non-isothermal rotating gas cloud system', Nonlinearity, 24, pp. 3165 - 3178, http://dx.doi.org/10.1088/0951-7715/24/11/009

Rogers CW; Schief WK, 2011, 'The pulsrodon in 2+1-dimensional magneto-gasdynamics: Hamiltonian structure and integrability', Journal of mathematical physics, 52, pp. 083701 (20pp), http://dx.doi.org/10.1063/1.3622595

Rogers C; Schief WK, 2010, 'Integrable Structure in the Theory of Stress Concentration in Shear-Strained Nonlinear Elastic Materials', STUDIES IN APPLIED MATHEMATICS, 125, pp. 39 - 53, http://dx.doi.org/10.1111/j.1467-9590.2009.00480

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