This page contains published works of Alexey Shevyakov and collaborators; the vast majority is available to download for research purposes. Use the menu to navigate to the section of interest.

My Google Scholar record: link

Ph.D. thesis	Symmetries and Exact Solutions of Plasma Equilibrium Equations [PDF] A. F. Cheviakov Queen's University at Kingston, 2004. Supervisor: Prof. O. I. Bogoyavlenskij
	Applications of Symmetry Methods to Partial Differential Equations (2010) G. W. Bluman, A. F. Cheviakov, and S. C. Anco Springer: Applied Mathematical Sciences, Vol. 168 ISBN 978-0-387-98612-8
	Analytical Properties of Nonlinear Partial Differential Equations, with Applications to Shallow Water Models (2024) Alexei Cheviakov, Peng Zhao Springer: CMS/CAIMS Books in Mathematics ISBN 978-3-031-53076-0

• K. Druzhkov and A.C. The relationship between two approximate symmetry frameworks. Physics Letters A 519 (2024): 129728 [PDF]
• J. Keller and A.C. Exact spherical vortex-type equilibrium flows in fluids and plasmas. Fundamental Plasma Physics 11 (2024): 100063 [PDF]
• J. Keller and A.C. New exact plasma equilibria with axial and helical symmetry. Physics of Plasmas 30, 092308 (2023) [PDF]
• A.C. and D. Dutykh. Galilei-invariant and energy-preserving extensions of Benjamin-Bona-Mahony-type equations. Partial Differential Equations in Applied Mathematics (2023) [PDF]
• M. R. Tarayrah, B. Pitzel and A.C. Two approximate symmetry frameworks for nonlinear partial differential equations with a small parameter: Comparisons, relations, approximate solutions. European Journal of Applied Mathematics (2022) [PDF]
• J. Gilbert & A.C. Global optimisation of the mean first passage time for narrow capture problems in elliptic domains. European Journal of Applied Mathematics (2022) [PDF]
• T. J. Black & A.C. 3DRSP: Matlab-based random sphere packing code in three dimensions. SoftwareX, 18 (2022): 101051 [PDF]
• M. R. Tarayrah and A.C. Relationship between unstable point symmetries and higher-order approximate symmetries of differential equations with a small parameter. Symmetry 13.9 (2021): 1612. [PDF]
• V. Srivastava and A.C. Brownian dynamics simulations for the narrow escape problem in the unit sphere. Physical Review E 104.6 (2021): 064113. [PDF]
• J.-F. Ganghoffer, R. Rahouadj, and A.C. Symmetry analysis and equivalence transformations for the construction and reduction of constitutive models. Advanced Modeling and Simulation in Engineering Sciences 8.1 (2021): 1-34. [PDF]
• A.C., D. Dutykh, and A. Assylbekuly. On Galilean invariant and energy preserving BBM-type equations. Symmetry 13.5 (2021): 878. [PDF]
• A.C., C. Lee, and R. Naz. Radial waves in fiber-reinforced axially symmetric hyperelastic media. Communications in Nonlinear Science and Numerical Simulation 95 (2021): 105649. [PDF]
• A.C., V. A. Dorodnitsyn, and E. I. Kaptsov. Invariant conservation law-preserving discretizations of linear and nonlinear wave equations. Journal of Mathematical Physics 61.8 (2020): 081504. [PDF]
• S. Anco and A.C. On the different types of global and local conservation laws for partial differential equations in three spatial dimensions: review and recent developments. International Journal of Non-Linear Mechanics (2020): 103569. [PDF]
• D. Dierkes, A.C., and M. Oberlack. New similarity reductions and exact solutions for helically symmetric viscous flows. Physics of Fluids 32.5 (2020): 053604. [PDF]
• R.O. Popovych and A.C. Variational symmetries and conservation laws of the wave equation in one space dimension. Applied Mathematics Letters 104 (2020): 106225. [PDF]
• W. Ridgway and A.C. Locally and globally optimal configurations of N particles on the sphere with applications in the narrow escape and narrow capture problems." Physical Review E 100.4 (2019): 042413. [PDF]
• R. Thiessen and A.C. Nonlinear dynamics of a viscous bubbly fluid. Communications in Nonlinear Science and Numerical Simulation 73 (2019): 244-264. [PDF]
• J. Gilbert and A.C. Globally optimal volume-trap arrangements for the narrow-capture problem inside a unit sphere. Physical Review E 99.1 (2019): 012109. [PDF]
• W. Ridgway and A.C. An iterative procedure for finding locally and globally optimal arrangements of particles on the unit sphere. Computer Physics Communications 233 (2018): 84-109. [PDF]
• A.C. Exact closed-form solutions of a fully nonlinear asymptotic two-fluid model. Physica D: Nonlinear Phenomena 370 (2018): 14-28. [PDF]
• J. Heß and A. C. A solution set-based entropy principle for constitutive modeling in mechanics. Continuum Mechanics and Thermodynamics 31.3 (2018): 775-806. [PDF]
• A. C. and J. Heß. A symbolic computation framework for constitutive modelling based on entropy principles, Applied Mathematics and Computation 324 (2018) 105-118. [PDF]
• A. C. Symbolic computation of equivalence transformations and parameter reduction for nonlinear physical models, Computer Physics Communications 220 (2017) 56-73 [PDF]
• R. Naz and A. C. Conservation laws and nonlocally related systems of two-dimensional boundary layer models. Zeitschrift für Naturforschung A 72, no. 11 (2017): 1031-1051 [PDF]
• A. C. and R. Naz. A recursion formula for the construction of local conservation laws of differential equations, Journal of Mathematical Analysis and Applications 448.1 (2017): 198–212 [PDF]
• A. C. and J.-F. Ganghoffer. One-dimensional nonlinear elastodynamic models and their local conservation laws with applications to biological membranes. Journal of the Mechanical Behavior of Biomedical Materials 58 (2016): 105-121 [PDF]
• A. C. and S. St. Jean. A comparison of conservation law construction approaches for the twodimensional incompressible Mooney-Rivlin hyperelasticity model. Journal of Mathematical Physics 56.12 (2015): 121505 [PDF]
  
• A. Nold, M. Oberlack and A. C. On new stability modes of plane canonical shear flows using symmetry classification. Journal of Mathematical Physics 56.11, (2015): 083514 [PDF]
• A. C., J.-F. Ganghoffer, and S. St.Jean. Fully non-linear wave models in fiber-reinforced anisotropic incompressible hyperelastic solids. International Journal of Non-Linear Mechanics 71 (2015): 8–21 [PDF]
• D. Gomez and A. C. Asymptotic analysis of narrow escape problems in nonspherical three-dimensional domains. Physical Review E 91 (2015): 012137 [PDF]
• A. C. and M. Oberlack. Generalized Ertel's theorem and infinite hierarchies of conserved quantities for three-dimensional time-dependent Euler and Navier-Stokes equations. Journal of Fluid Mechanics 760 (2014): 368-386 [PDF]
• Z. Yang and A. C. Some relations between symmetries of nonlocally related systems. Journal of Mathematical Physics 55 (2014): 083514 [PDF]
• A. C. Conservation properties and potential systems of vorticity-type equations. Journal of Mathematical Physics 55 (2014): 033508 [PDF]
• A. C. Symbolic computation of nonlocal symmetries and nonlocal conservation laws of partial differential equations using the GeM package for Maple. Similarity and Symmetry Methods, Lecture Notes 165 in Applied and Computational Mechanics 73, Springer (2014). [PDF]
• A. C., J.-F. Ganghoffer, and R. Rahouadj. Finite strain plasticity models revealed by symmetries and integrating factors: The case of Dafalias spin model. International Journal of Plasticity 44 (2013): 47–67 [PDF]
• O. Kelbin, A. C., and M. Oberlack. New conservation laws of helically symmetric, plane and rotationally symmetric viscous and inviscid flows. Journal of Fluid Mechanics 721 (2013): 340-366 [PDF]
• A. C. and D. Zawada. Narrow-escape problem for the unit sphere: Homogenization limit, optimal arrangements of large numbers of traps, and the N^2 conjecture. Physical Review E 87 (2013): 042118 [PDF]
• C. Kallendorf, A. C., M. Oberlack, and Y. Wang. Conservation laws of surfactant transport equations. Physics of Fluids 24 (2012): 102105 [PDF]
• A. C,  J.-F. Ganghoffer. Symmetry properties of two-dimensional Ciarlet-Mooney-Rivlin constitutive models in nonlinear elastodynamics. Journal of Mathematical Analysis and Applications 396 (2012): 625–639 [PDF]
• A. S. Reimer, A. C. A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet–Neumann boundary conditions. Computer Physics Communications 184 (2012): 783–798 [PDF]
• A. C., A. S. Reimer, M. J. Ward. Mathematical modeling and numerical computation of narrow escape problems. Physical Review E 85 (2012): 021131 [PDF]
• A. C. Symbolic Computation of local symmetries of nonlinear and linear partial and ordinary differential equations. Mathematics in Computer Science 4 (2010): 203–222 [PDF]
• A. Nold, M. Oberlack and A. C. Applications of symmetry analysis in stability theory. Numerical & Experimental Fluid Mechanics VII, NNFM 112 (2010): pp. 257–264. [PDF]
• A. C. and G. W. Bluman. Multi-dimensional PDE systems: generating new systems via conservation laws, potentials, gauges, subsystems. Journal of Mathematical Physics 51 (2010): 103521 [PDF]
• A. C. and G. W. Bluman. Multi-dimensional PDE systems: nonlocal symmetries, nonlocal conservation laws, exact solutions. Journal of Mathematical Physics 51 (2010): 103522 [PDF]
• A. C. and G. W. Bluman. On locally and nonlocally related potential systems. Journal of Mathematical Physics 51 (2010): 073502 [PDF]
• A. C., M. J. Ward, and R. Straube. An asymptotic analysis of the mean first passage time for narrow escape problems: Part II: the sphere. SIAM Multiscale Modeling and Simulation 8.3 (2010): 836-870 [PDF]
• A. C. and M. J. Ward. Optimizing the Principal Eigenvalue of the Laplacian in a Sphere with Interior Traps. Mathematical and Computer Modelling (2010) [PDF]
• A. C., Computation of fluxes of conservation laws. Journal of Engineering Mathematics 66 (2010): 153–173 [PDF]
• M. Oberlack and A. C.. Higher-order symmetries and conservation laws of the G-equation for premixed combustion and resulting numerical schemes. Journal of Engineering Mathematics 66 (2010): 121–140 [PDF]
• G. W. Bluman, A. C., and J.-F. Ganghoffer. On the nonlocal symmetries, group invariant solutions and conservation laws of the equations of nonlinear dynamical compressible elasticity. Proc. IUTAM (2009) [PDF]
• A. C. and J. Hartwick. Constant per capita consumption paths with exhaustible resources and decaying produced capital. Ecological Economics 68 (2009): 2969–2973 [PDF]
• G. W. Bluman, A. C., 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. C., An extended procedure for finding exact solutions of partial differential equations arising from potential symmetries. Applications to gas dynamics. Journal of Mathematical Physics 49 (2008): 083502 [PDF]
• G. Bluman, A. C., and J.-F. Ganghoffer. Nonlocally related PDE systems for one-dimensional nonlinear elastodynamics, Journal of Engineering Mathematics 62 (2008): 203–221 [PDF]
• G. Bluman, A. C., and M. Senthilvelan. Solution and asymptotic/blow-up behaviour of a class of nonlinear dissipative systems. Journal of Mathematical Analysis and Applications 339 (2008): 1199-1209 [PDF]
• A. C. and S. C. Anco. Analytical properties and exact solutions of static plasma equilibrium systems in three dimensions. Physics Letters A 372 (2008): 1363-1373 [PDF]
• A. C. 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. C. Nonlocally related systems, linearization and nonlocal symmetries for the nonlinear wave equation, Journal of Mathematical Analysis and Applications 333 (2007): 93-111 [PDF]
• A. C. GeM software package for computation of symmetries and conservation laws of differential equations. Computer Physics Communications 176 (2007): 48-61  [PDF]
• G. Bluman , A. C., and N. M. Ivanona. Framework for nonlocally related PDE systems: simplification; new symmetries and conservation laws for NLT equations. Journal of Mathematical Physics 47 (2006): 113505 [PDF]
• G. Bluman  and A. C. Framework for potential systems and nonlocal symmetries: Algorithmic approach. Journal of Mathematical Physics 46 (2005): 123506 [PDF]
• A. C. Construction of exact plasma equilibrium solutions with different geometries. Physical Review Letters 94 (2005): 165001 [PDF]
• A. C. and J. Hartwick. Beckmann's Edgeworth-Bertrand duopoly example revisited. International Game Theory Review 7 (4) (2005): 461-471 [PDF]
• A. C. Analytical 3-dimensional anisotropic magnetohydrodynamic equilibria. Topology and its Applications 152 (2005): 157–173 [PDF]
  
• A. C. 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. C. and O. I. Bogoyavlenskij. Exact anisotropic MHD equilibria. Journal of Physics A 37 (2004): 7593-7607 [PDF]
• A. C. Bogoyavlenskij symmetries of ideal MHD equilibria as Lie point transformations. Physics Letters A 321 (2004): 34-49 [PDF]
• A. C. Bogoyavlenskij symmetries of isotropic and anisotropic MHD equilibria are Lie point transformations. Proc. Inst. Math. NAS Ukraine, 50 (2004): 69-76 [PDF]
• N. A. Kudryashov, G. S.  Romanov, and A. C. Numerical modeling of the quasistationary regime of eruption of a volcano at the initial stage. Engineering-Physics Journal (Russian) / JEPTER (English) 76 (2003): 795-803 [PDF]
• N. A. Kudryashov, G. S.  Romanov and A. C. Numerical modeling of explosive volcanic eruption in the initial stage. Engineering-Physics Journal (Russian) / JEPTER (English) 75 (2002): 521-528 [PDF]
  
• N. A. Kudryashov and A. C. Self-similar solutions of one-dimentional problems of gas filtration with a quadratic resistance law. Engineering-Physics Journal (Rus) / JEPTER (Eng) 72 (1999): 1090-1099 [PDF]
  

arXiv preprints, authored and co-authored: link

• "New Exact Axially and Helically Symmetric Solutions to Plasma Equilibrium Equations," LaPlas conference 2024 [PDF]
• "Approximate Symmetries and Conservation Laws; their Applications to PDEs," Applications of Computer Algebra ACA'2023, July 2023 [PDF]
• "New exact plasma equilibria with axial and helical symmetry," CMS Winter meeting December 2023 [PDF]
• "Conservation laws of differential equations: computation, connections, and applications," Mathematics colloquium, Université Laval, October 2023 [PDF]
• "New analytical solutions of static and dynamic plasma equilibrium equations in axial and helical symmetry," Modern Achievements in Symmetries of Differential Equations, Suranaree University of Technology, December 2022 [PDF]
• "Analytical properties of nonlinear partial differential equations in shallow water theory and beyond," CMS Winter meeting December 2022, Toronto [PDF]
• "Two approximate symmetry frameworks for nonlinear DEs with a small parameter. Comparisons, relations, approximate solutions," Symmetry, Invariants, and their Applications, Halifax, August 5, 2022 [PDF]
• "Symmetry Properties of a Family of Benjamin-Bona-Mahony-type Equations," Analytical and Numerical Methods in Differential Equations (ANMDE 2021 and Yanenko 100), August 23-26, 2021 [PDF]
• "Narrow Escape and Narrow Capture Problems in Three Dimensions: Modeling, Analysis, Optimization of Trap Configurations," PIMS Workshop on New Trends in Localized Patterns in PDEs, May 10-13, 2021 [PDF]
• "Conservation laws, similarity reductions and exact solutions for helically symmetric incompressible fluid flows," online Applied Mathematics Seminar, U. of Washington, USA, 14 May 2020 [PDF]
• "Symbolic Computation of Symmetries and First Integrals in Dynamical Systems," Winter CMS Meeting, December 8, 2019, Toronto, Canada [PDF]
• "Conservation laws, similarity reductions and exact solutions for helically symmetric incompressible fluid flows," Colloquium, Fudan University, June 2019 [PDF]
• "Narrow Escape and Narrow Capture problems in 3D, asymptotic solutions, optimal trap configurations", IMACS Nonlinear Waves, Athens, GA, USA, April 18, 2019 [PDF]
• "Exact Solutions of a Fully Nonlinear Two-Fluid Model", Keldysh Inst. for Applied Math., Moscow, Russia, June 28, 2018 [PDF]
• "The Narrow Escape Problem for the Unit Sphere and Other 3D Domains: Asymptotic Solution, Homogenization Limit, and Optimal Trap Arrangements", Conference "Problems of Mathematical Physics and Mathematical Modelling", MEPhI,  Moscow, Russia, June 26, 2018 [PDF]
• "Global and local conservation laws for physical models: Cases of static and moving domains." Seminar, TU Darmstadt, May 18, 2018 [PDF]
• Topical School on ‘Symmetry, similarity methods and conservation laws in solid and fluid mechanics’, Cargese, France, 2018
  • A.C. Talk 1: Symmetries of Differential Equations: Symbolic Computation using Maple [PDF]
  • A.C. Talk 2: On Symmetries of Linear and Nonlinear PDEs [PDF]
  • A.C. Talk 3: Equivalence Transformations and Their Symbolic Computation [PDF]
  • A.C. Talk 4: Symmetries of Differential Equations: Practical session [PDF]
• "Conservation Laws of Differential Equations: Origins, Modern Approach, Properties, Systematic Computation, and Applications" McMaster University Colloquium, LAMA/CNRS (Chambery, France) talk, 10/2017 [PDF]
• "Local and Global Optimization of Particle Locations on the Sphere: Models, Applications, Mathematical Aspects, and Computations." SIAM DS17 meeting, Snowbird, Utah, May 2017 [PDF]
• "Conservation laws of vorticity-type equations", Canadian Mathematical Society (CMS) 2016 Summer meeting, Edmonton, Canada, May 25, 2016 [PDF]
• "Nonlinear Elastodynamic Models of Wave Propagation and Conservation Laws for Fiber-Reinforced Materials", Society for Industrial and Applied Mathematics (SIAM) Meeting 2016, Philadelphia, USA, May 11, 2016 [PDF]
• "Conservation Laws of Fluid Dynamics Models", Seminar, Shanghai Maritime University, China, June 2015 [PDF]
• "Local Conservation Laws for Nonlinear Models: Theory, Systematic Construction, and Computation Examples", Seminar, Shanghai Maritime University and the University of Shanghai, China, June 2015 [PDF]
• "Asymptotic Analysis of Narrow Escape Problems in Non-Spherical 3D Domains" [joint with D. Gomez], SIAM Conference on Applications of Dynamical Systems, Snowbird, Utah, May 2015 [PDF]
• "Conservation Laws of Models of Biological Membranes in the Framework of Nonlinear Elastodynamics" [Joint with J.-F. Ganghoffer], Euromech 560 Colloquium, Ascona, Switzerland, Feb. 2015 [PDF]
• "On Conservation Laws and Potential Systems of Vorticity-Type Equations", GADEIS VII, Cyprus, June 2014 [PDF]
• "Constitutive Relations, Natural States, and Traveling Waves in Two-Dimensional Nonlinear Elastodynamics", CMSC 2014, University of Saskatchewan, June 2014 [PDF]
• "Conservation Laws For Viscous and Inviscid Flows in Helical, Plane and Rotational Symmetry", IMACS Nonlinear Waves Conference, UGA, Athens, GA, March 25, 2013 [PDF]
• "A Maple-based Package for Computation of Conservation Laws, Symmetries and Invariant forms of DEs", ICIAM 2011, Vancouver [PDF]
• "An extended procedure for finding exact solutions of PDEs arising from potential symmetries", Symmetry in Nonlinear Mathematical Physics, Kiev, 2009 [PDF]