Publications - Topics

Department of Mathematics




Publications - Topics


top

CONSERVATION LAWS

  • New conservation laws obtained directly from symmetry action on a known conservation laws. (with G. Bluman and Temuerchaolu) J. Math. Anal. Appl. 322 (2006), 233--250.
  • Symmetries, conservation laws, and cohomology of Maxwell's equations using potentials. (with D. The) Acta Appl. Math. 89 (2005), 1--52.
  • Symmetries and currents of massless neutrino fields, electromagnetic and graviton fields. (with J. Pohjanpelto) in CRM Proceedings and Lecture Notes, Vol. 34, "Workshop on Symmetry in Physics" (2004), 1--12.
  • Conserved currents of massless spin s fields. (with J. Pohjanpelto) Proc. Roy. Soc. 459 (2003), 1215--1239.
  • Conservation laws of scaling-invariant field equations. J. Phys. A: Math. and Gen. 36 (2003), 8623--8638.
  • Direct construction method for conservation laws of partial differential equations II: General treatment. (with G. Bluman) Euro. Jour. Appl. Math. 13 (2002), 567--585.
  • 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.
  • Classification of local conservation laws of Maxwell's equations. (with J. Pohjanpelto) Acta. Appl. Math. 69 (2001), 285--327.
  • Integrating factors and first integrals of ordinary differential equations. (with G. Bluman) Euro. Jour. Appl. Math. 9 (1998), 245--259.
  • Direct construction of conservation laws from field equations. (with G. Bluman) Phys. Rev. Lett. 78 (1997), 2869--2873.
  • Derivation of conservation laws from nonlocal symmetries of differential equations. (with G. Bluman) J. Math. Phys. 37 (1996), 2361--2375.

Top

SYMMETRY METHODS AND ANALYSIS

  • Conservation laws and symmetries of semilinear radial wave equations. (with N. Ivanova), J. Math. Anal. Appl. 332 (2006), 863-876.
  • Exact solutions of semilinear radial wave equations in n dimensions. (with Sheng Liu) J. Math. Analysis Appl. 297 (2004), 317--342.
  • Nonlocal symmetries and conservation laws of Maxwell's equations. (with G. Bluman) J. Math. Phys. 38 (1997), 3508--3532.

Top

INTEGRABILITY AND SOLITONS

  • 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).
  • 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).
  • Bi-Hamiltonian operators, integrable flows of curves using moving frames, and geometric map equations. J. Phys. A: Math. Gen. 39 (2006), 2043--2072.
  • Some symmetry classifications of hyperbolic vector evolution equations. (with T. Wolf) J. Nonlinear Math. Phys. 12, Supplement 1 (2005), 13--31.

Top

CLASSICAL GAUGE THEORY

  • Gauge theory deformations and novel Yang-Mills Chern-Simon field theories with torsion. Int. J. Geometric Methods in Modern Physics 1 (2004), 493--544.
  • Parity violating spin-two gauge theories. Phys. Rev. D 67 (2003), 124007 (8 pages).
  • Exotic Yang-Mills dilaton gauge theories. Lett. Math. Phys. 62 (2002), 245--258.
  • On multi-graviton and multi-gravitino gauge theories. Class. Quant. Grav. 19 (2002), 6445--6467.
  • Nonlinear gauge theories of a spin-two field and a spin-three-halves field. Ann. Phys. 270 (1998), 52--125.
  • Novel generalization of three dimensional Yang-Mills theory. J. Math. Phys. 38 (1997), 3399--3413
  • New spin-one gauge theory in three dimensions. J. Math. Phys. 36 (1995), 6553--6565.
  • Non-Grassmann generalization of classical supergravity theory. Phys. Rev. D 50 (1994), 2648--2661.
  • Construction of locally-symmetric Lagrangian field theories from variational identities. Contemp. Math. (Amer. Math. Soc.) 132 (1992), 27--50

Top

GENERAL RELATIVITY

  • Mean curvature flow and quasilocal mass for spacelike two-surfaces in Hamiltonian General Relativity. J. Math. Phys. 48 (2007) 052502 (32 pages).
  • Covariant Hamiltonian boundary conditions in General Relativity for spatially bounded spacetime regions. (with R. Tung) J. Math. Physics 43 (2002), 5531--5566.
  • Properties of the symplectic structure of General Relativity for spatially bounded spacetime regions. (with R. Tung) J. Math. Physics 43 (2002), 3984--4019.

Top

MATHEMATICAL PHYSICS

  • 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.
  • Global existence for wave maps with torsion. (with J. Isenberg) Comm. Partial Diff. Eqns. 25 (2000), 1669--1702.
  • Does there exist a sensible quantum theory of an algebra-valued scalar field? (with R.M. Wald) Phys. Rev. D 39 (1989), 2297--2307.

 Top