Michal Marvan

Assistant Professor at the Silesian University in Opava

• Undergraduate study at J.E. Purkyne University, Brno, Department of Mathematics (1976–1981).
• Graduate study at Moscow State University, Chair of Higher Geometry and Topology (1983–1987).
• Ph.D. Thesis: "Horizontal cohomology with general coefficients" (A. M. Vinogradov, Moscow, 1989)

Research Topics

The keyword is diffiety, an object of the category of differential equations, introduced by A. M. Vinogradov at the end of seventies. The diffiety structure determines symmetries, conservation laws, zero-curvature representations, recursion operators, Backlund transformations, and many invariants of partial differential equations.

Related Publications

• M. Marvan, Recursion operators for the Einstein equations with symmetries, in: Proc. Conf. ``Symmetry in Nonlinear Mathematical Physics,'' Kyiv, Ukraine, June 23–28, 2003. Proc. Inst. Math. NAS Ukraine 50 (2004), Part I, 179–183.
• M. Marvan, Reducibility of zero curvature representations with application to recursion operators, Acta Appl. Math., 83 (2004) 39–68. Preprints: DIPS 03/2003 and nlin.SI/0306006.
• M. Marvan and A. Sergyeyev, Recursion operator for the Nizhnik–Veselov–Novikov equation, J. Phys. A: Math. Gen. 36 (2003) L87–L92. Full text freely available from stacks.iop.org/0305-4470/36/L87.
• M. Marvan, Scalar second order evolution equations possessing an irreducible sl₂-valued zero curvature representation, J. Phys. A: Math. Gen. 35 (2002) 9431–9439; preprint DIPS–4/2002; LANL nlin.SI/0203043.
• Michal Marvan, On the horizontal gauge cohomology and non-removability of the spectral parameter, Acta Appl. Math. 72 (2002) 51–65.
• M. Marvan, Geometric Aspects of S-Integrability, Proc. Seminar on Differential Geometry, Math. Publications 2 (Silesian Univ. Opava, Opava, 2000) 131–144.
• I.S. Krasil'shchik and M. Marvan, Coverings and integrability of the Gauss–Mainardi–Codazzi equations, Acta Appl. Math. 56 (1999) 217–230, LANL solv-int/9812010
• M. Marvan, Some local properties of Baecklund relations, Acta Appl. Math. 54 (1998) 1–25.
• M. Marvan, A direct procedure to compute zero-curvature representations. The case sl₂, in: Proc. Conf. Secondary Calculus and Cohomological Physics, Moscow. ELibEMS
• M. Marvan, Another look on recursion operators, in: Differential Geometry and Applications, Proc. Conf. Brno, 1995 (Masaryk University, Brno, 1996). ELibEMS
• M. Marvan, On zero curvature representations of partial differential equations, in: Differential Geometry and Its Applications, Proc. Conf. Opava, Czechoslovakia, Aug. 24–28, 1992 (Silesian University, Opava, 1993) 103–122. ELibEMS
• M. Marvan, On the C-spectral sequence with "general" coefficients, in: Differential Geometry and Its Applications, Proc. Conf. Brno, Czechoslovakia, Aug. 27–Sept. 2, 1989 (World Scientific, Singapore, 1990) 361–371.
• M. Marvan, On the horizontal cohomology with general coefficients, Rend. Circ. Mat. Palermo Ser. II, 22 (1989) Suppl., 161–170.
• M. Marvan, A note on the category of partial differential equations, in: Differential Geometry and its Applications (Communications), Proc. Conf. Brno, Czechoslovakia, Aug. 24–30, 1986 (J.E. Purkyne Univ., Brno, 1987) 235–244.

Software Project

• Jets – a set of Maple procedures for routine computations on jet spaces and diffieties. Emphasis is laid on solution of equations in total derivatives, such as those determining infinitesimal symmetries, generating functions of conservation laws, zero-curvature representations, recursion operators, Backlund transformations, etc.

Last updated:October 22, 2004.