Publications - Chonological

Books

• G.W. Bluman and S.C. Anco,
  Symmetry and Integration Methods for Differential Equations,
  Applied Mathematical Sciences, volume 154, Springer (New York) 2002.
  More information

  "...for anyone wishing to master techniques for obtaining first integrals of ODEs, this book is outstanding."
  Book Review by Prof. Peter Hydon, UK Nonlinear News, May 2003.

Preprints

• Group-invariant soliton equations and bi-Hamiltonian geometric curve flows in Riemannian symmetric spaces.
  Submitted to J. Geom. Phys. (2007)
  e-print archive: www.arXiv.org/abs/nlin.SI/0703041
• Curve flows in Lagrange-Finsler geometry, bi-Hamiltonian structures and solitons.  (with S. Vacaru)
  Submitted to J. Phys. A (2006)
  e-print archive: www.arXiv.org/abs/math-ph/0609070
  
• Analytical properties and exact solutions of static plasma equilibrium systems in three dimensions. (with A. Cheviakov).
  Submitted to Phys. Lett. A (206).

Journal Articles and Refereed Conference Proceedings

• Spinor derivation of quasilocal mean curvature mass in General Relativity.
  To appear in Inter. J. Theor. Phys. (2007).
• Hamiltonian curve flows in Lie groups G \subset U(N) and vector NLS, mKdV, sine-Gordon soliton equations.
  To appear in Proceedings of IMA Workshop on Symmetries and Overdetermined Systems of Partial Differential Equations (2006)
  eprint archive: www.arXiv.org/abs/nlin.SI/0610075
• Mean curvature flow and quasilocal mass for 2-surfaces in Hamiltonian General Relativity. J. Math. Phys. 48, (2007) 052502 (32 pages).
  e-print archive: www.arXiv.org/abs/gr-qc/0402057
• Conservation laws and symmetries of semilinear radial wave equations. (with N. Ivanova), J. Math. Anal. Appl. 332 (2006), 863-876.
  e-print archive: www.arXiv.org/abs/math-ph/0608037
• Some Penrose transforms in complex differential geometry. (with J.Bland and M. Eastwood) Science in China Series A: Mathematics (2006) Vol. 49 No. 11, 1599-1610.
• New conservation laws obtained directly from symmetry action on known conservation laws. (with G. Bluman and Temuerchaolu)
  J. Math. Anal. Appl. 322 (2006), 233-250.
• Hamiltonian flows of curves in symmetric spaces G/SO(N) and vector soliton equations of mKdV and sine-Gordon type.
  SIGMA, Vol. 2 (2006), Paper 044 (18 pages).
  e-print archive: www.arXiv.org/abs/nlin.SI/0512046
• Bi-Hamiltonian operators, integrable flows of curves using moving frames, and geometric map equations.
  J. Phys. A: Math. Gen. 39 (2006), 2043-2072.
  e-print archive: www.arXiv.org/abs/nlin.SI/0512051
• Symmetries, conservation laws, and cohomology of Maxwell's equations using potentials. (with D. The)
  Acta Appl. Math. 89 (2005), 1-52
  e-print archive: www.arXiv.org/abs/math-ph/0501052
• Some symmetry classifications of hyperbolic vector evolution equations. (with T. Wolf)
  J. Nonlinear Math. Phys. 12, Supplement 1 (2005), 13-31;
  erratum, J. Nonlinear Math. Phys. 12 (2005), 607-608.
  e-print archive: www.arXiv.org/abs/nlin.SI/0412015
• Gauge theory deformations and novel Yang-Mills Chern-Simon field theories with torsion.
  Int. J. Geometric Methods in Modern Physics 1 (2004), 493-544.
  Special issue on "Advanced Geometric Techniques in Gauge Theory".
  e-print archive: www.arXiv.org/abs/math-ph/0407026
• Exact solutions of semilinear radial wave equations in n dimensions. (with Sheng Liu)
  J. Math. Analysis Appl. 297 (2004), 317-342.
  e-print archive: www.arXiv.org/abs/math-ph/0309049
• Symmetries and currents of massless neutrino fields, electromagnetic and graviton fields. (with J. Pohjanpelto)
  in CRM Proceedings and Lecture Notes, Volume 34, "Workshop on Symmetry in Physics" (2004), 1-12.
  e-print archive: www.arXiv.org/abs/math-ph/0306072
• Parity violating spin-two gauge theories.
  Phys. Rev. D 67 (2003), 124007, 17 pages.
  e-print archive: www.arXiv.org/abs/gr-qc/0305026
• Conservation laws of scaling-invariant field equations.
  J. Phys. A: Math. and Gen. 36 (2003), 8623-8638.
  e-print archive: www.arXiv.org/abs/math-ph/0303066
• Gauge theories of Yang-Mills vector fields coupled to antisymmetric tensor fields.
  J. Math. Phys. 44 (2003), 1006-1043.
  e-print archive: www.arXiv.org/abs/math-ph/0209051
• Conserved currents of massless spin s fields. (with J. Pohjanpelto)
  Proc. Roy. Soc. 459 (2003), 1215-1239.
  e-print archive: www.arXiv.org/abs/math-ph/0202019
• On multi-graviton and multi-gravitino gauge theories.
  Class. Quant. Grav. 19 (2002), 6445-6467.
  e-print archive: www.arXiv.org/abs/gr-qc/0303033
• Exotic Yang-Mills dilaton gauge theories.
  Lett. Math. Phys. 62 (2002), 245-258.
  e-print archive: www.arXiv.org/abs/math-ph/0209052
• Covariant Hamiltonian boundary conditions in General Relativity for spatially bounded spacetime regions. (with R. Tung)
  J. Math. Physics 43 (2002), 5531-5566.
  e-print archive: www.arXiv.org/abs/gr-qc/0109013
• Properties of the symplectic structure of General Relativity for spatially bounded spacetime regions. (with R. Tung)
  J. Math. Physics 43 (2002), 3984-4019.
  e-print archive: www.arXiv.org/abs/gr-qc/0109014
• Direct construction method for conservation laws of partial differential equations II: General treatment. (with G. Bluman)
  Euro. Jour. Appl. Math. 13 (2002), 567-585.
  e-print archive: www.arXiv.org/abs/math-ph/0108024
• Direct construction method for conservation laws of partial differential equations I: Examples of conservation law classifications. (with G. Bluman)
  Euro. Jour. Appl. Math. 13 (2002), 545-566.
  e-print archive: www.arXiv.org/abs/math-ph/0108023
• Classification of local conservation laws of Maxwell's equations. (with J. Pohjanpelto)
  Acta. Appl. Math. 69, 285-327 (2001).
  e-print archive: www.arXiv.org/abs/math-ph/0108017
• Global existence for wave maps with torsion. (with J. Isenberg)
  Comm. Partial Diff. Eqs. 25, 1669-1702 (2000).
  e-print archive: www.arXiv.org/abs/math-ph/0007032
• Nonlinear gauge theories of a spin-two field and a spin-three-halves field.
  Ann. Phys. 270, 52-125 (1998).
  postscript      pdf
• Integrating factors and first integrals of ordinary differential equations. (with G. Bluman)
  Eur. Jour. Appl. Math. 9, 245-259 (1998).
• Novel generalization of three dimensional Yang-Mills theory.
  J. Math. Phys. 38, 3399-3413 (1997).
  e-print archive: www.arXiv.org/abs/math-ph/0209050
• Nonlocal symmetries and conservation laws of Maxwell's equations. (with G. Bluman)
  J. Math. Phys. 38, 3508-3532 (1997).
  postscript      pdf
• Direct construction of conservation laws from field equations. (with G. Bluman)
  Phys. Rev. Lett. 78, 2869-2873 (1997).
  postscript      pdf
• Derivation of conservation laws from nonlocal symmetries of differential equations. (with G. Bluman)
  J. Math. Phys. 37, 2361-2375 (1996).
  postscript      pdf
• New spin-one gauge theory in three dimensions.
  J. Math. Phys. 36, 6553-6565 (1995).
  postscript      pdf
• Non-Grassmann generalization of classical supergravity theory.
  Phys. Rev. D 50, 2648-2661 (1994).
  postscript      pdf
• Construction of locally-symmetric Lagrangian field theories from variational identities.
  Contemp. Math. (Amer. Math. Soc.) 132, 27-50 (1992).
  postscript      pdf
• Does there exist a sensible quantum theory of an algebra-valued scalar field? (with R.M. Wald)
  Phys. Rev. D 39, 2297-2307 (1989).