- Mathematical modelling;
- Symmetry methods for analysis of partial and differential equations;
- Scientific Computation (symbolic and numerical).

- "Computation of Point Symmetries Admitted by DEs", TU Darmstadt, May 2008 [PPT]
- "Computation of Conservation Laws Admitted by PDEs", TU Darmstadt, May 2008 [PPT]
- "Nonlocally Related PDE Systems", TU Darmstadt, May 2008 [PPT]
- "Computation and applications of local conservation laws", PNRMS, University of Saskatchewan, 2009 [PPT]

- A. F. Cheviakov, M. J. Ward, and R. Straube, An Asymptotic
Analysis of the Mean First Passage Time for Narrow Escape Problems: Part II:
The Sphere. [PDF]

(Submitted for SIAM Multiscale Modeling and Simulation, 2009) - A. F. Cheviakov and M. J. Ward, Optimizing the
Principal Eigenvalue of the Laplacian in a Sphere
with Interior Traps. [PDF]

(Submitted for the special issue of Mathematical and Computer Modeling based on the international meeting \Mathematical Methods and Modeling in the Biological Sciences", held in Rio de Janiero, March 2009.) - M. Oberlack and A. F. Cheviakov, Higher-order symmetries and conservation laws of the G-equation for premixed combustion and resulting numerical schemes, J. Eng. Math. (2009). [PDF]
- G. W. Bluman, A. F. Cheviakov, and J.-F.
Ganghoffer, On the nonlocal symmetries, group invariant
solutions and conservation laws of the equations of nonlinear dynamical
compressible elasticity, Accepted to Proc.

IUTAM (2009). [PDF] - A. F. Cheviakov and J. Hartwick, Constant Per Capita Consumption Paths with Exhaustible Resources and Decaying Produced Capital, Accepted to Ecological Economics (2009). [PDF]
- A. F. Cheviakov, Computation of fluxes of conservation laws, J. Eng. Math. (2009), DOI: 10.1007/s10665-009-9307-x [PDF]
- G. W. Bluman, A. F. Cheviakov, and S. C. Anco, Construction of
Conservation Laws: How the Direct Method Generalizes
Noether's Theorem, Proc. 4th Workshop ``Group Analysis of Differential
Equations &

Integrability'' (2009), 1-23. [PDF] - A. F. Cheviakov, An extended procedure for finding exact solutions of partial differential equations arising from potential symmetries. Applications to gas dynamics, J. Math. Phys. 49, (2008), 083502 [PDF]
- G. Bluman, A. F. Cheviakov, and J.-F. Ganghoffer, Nonlocally related PDE systems for one-dimensional nonlinear elastodynamics, J. Eng. Math., online DOI 10.1007/s10665-008-9221-7 (2008). [PDF]
- G. Bluman, A. F. Cheviakov, and M. Senthilvelan, Solution andAsymptotic/Blow-up Behaviour of a Class of Nonlinear Dissipative Systems, J. Math. An. App. 339 (2008), 1199--1209. [PDF]
- A. F. Cheviakov and S. C. Anco, Analytical properties and exact solutions of static plasma equilibrium systems in three dimensions, Phys. Lett. A 372 (2008) 1363--1373. [PDF]
- A. F. Cheviakov and M. J. Ward, A Two--Dimensional Metastable Flame-Front and a Degenerate Spike--Layer Problem, Interfaces and Free Boundaries 9 (2007), 513--547. [PDF]
- G. Bluman and A. F. Cheviakov, Nonlocally related systems, linearization and nonlocal symmetries for the nonlinear wave equation, J. Math. An. App. 333 (2007), 93--111. [PDF]
- A. F. Cheviakov, “GeM software package for computation of symmetries and conservation laws of differential equations”. Comp. Phys. Comm. 176 (2007) 48–-61 [PDF]
- G. Bluman , A. F. Cheviakov, and N. M. Ivanona, “Framework for nonlocally related PDE systems: simplification; new symmetries and conservation laws for NLT equations,” J. Math. Phys. 47 (2006), 113505. [PDF]
- G. Bluman and A. F. Cheviakov “Framework for potential systems and nonlocal symmetries: Algorithmic approach,” J. Math. Phys. 46, 123506 (2005) [PDF]
- A. F. Cheviakov “Construction of exact plasma equilibrium solutions with different geometries,” Phys. Rev. Lett. 94, 165001 (2005) [PDF]
- A. F. Cheviakov and J. Hartwick "Beckmann's Edgeworth-Bertrand Duopoly Example Revisited." Int. Game Theory Rev. 7 (4), 461-471 (2005) .
- A. F. Cheviakov “Analytical 3-Dimensional Anisotropic Magnetohydrodynamic Equilibria.” Topology and its Applications 152, 157–173 (2005).
- A. F. Cheviakov “Exact plasma equilibria from symmetries and transformations of MHD and CGL equilibrium equations,” in: “Symmetry Methods in Physics” (ed. C.Burdik, O.Navratil, S.Posta), Prague, Czech Rep., ISBN 5-9530-0069-3 (2004) [PDF]
- A. F. Cheviakov and O. I. Bogoyavlenskij “Exact anisotropic MHD equilibria”, J. Phys. A 37, 7593 – 7607 (2004) [PDF]
- A. F. Cheviakov “Bogoyavlenskij symmetries of ideal MHD equilibria as Lie point transformations,” Phys. Lett. A 321, 34-49 (2004) [PDF]
- A. F. Cheviakov “Bogoyavlenskij symmetries of isotropic and anisotropic MHD equilibria are Lie point transformations”, Proc. Inst. Math. NAS Ukraine, 50, 69-76 (2004) [PDF]
- N. A. Kudryashov, G. S. Romanov, and A. F. Cheviakov, “Numerical simulation of the quasistationary phase of a volcanic eruption in the initial stage”, Engineering-Physics Journal (Russian) / JEPTER (English) 76, 795-803 (2003) [PDF]
- N. A. Kudryashov, G. S. Romanov and A. F. Cheviakov “Numerical modeling of explosive volcanic eruptions”, Eng.-Phys. J. (Rus) / JEPTER (Eng). 75, 521-528 (2002).
- N. A. Kudryashov and A. F. Cheviakov “Self-Similar Solutions of 1-Dimentional Problems of Gas Filtration with Square Law of Resistance,” Eng.-Phys. J. (Rus) / JEPTER (Eng). 72, 1090-1099 (1999).

*Last updated: Feb 2009*