Publications - By Topic

Department of Mathematics




Publications - By Topic


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Conserved Integrals/Conservation Laws of PDEs

  • New conserved vorticity integrals for moving surfaces in multi-dimensional fluid flow.
    J. Math. Fluid Mech. 15 (2013), 439-451.
  • Conservation laws and symmetries of quasilinear radial wave equations in multi-dimensions. (with S. MacNaughton and T. Wolf)
    J. Math. Phys. 53 (2012), 053703 (33 pages).
  • Conservation laws of inviscid non-isentropic compressible fluid flow in n>1 spatial dimensions. (with A. Dar)
    Proc. Roy. Soc. A 466 (2010), 2605-2632.
  • Classification of conservation laws of compressible isentropic fluid flow in $n>1$ spatial dimensions. (with A. Dar)
    Proc. Roy. Soc. A 465 (2009), 2461-2488.
  • Construction of conservation laws: How the Direct Method generalizes Noether's theorem. (with G. Bluman and A. Cheviakov)
    in Group Analysis of Differential Equations and Integrable Systems (2008), 13-35.
  • Invertible mappings of nonlinear PDEs to linear PDEs through admitted
    conservation laws. (with G. Bluman and T. Wolf)
    Acta Appl. Math. 101 (2008), 21-38.
  • Conservation laws and symmetries of semilinear radial wave equations. (with N. Ivanova)
    J. Math. Anal. Appl. 332 (2006), 863-876.
  • 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 (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. J. 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. J. 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. Jr. Appl. Math. 9 (1998), 245-259.
  • Direct construction of conservation laws from field equations. (with G. Bluman)
    Phys. Rev. Lett. 78 (1997), 2869-2873.
  • Nonlocal symmetries and conservation laws of Maxwell's equations. (with G. Bluman)
    J. Math. Phys. 38 (1997), 3508-3532.
  • Derivation of conservation laws from nonlocal symmetries of differential equations. (with G. Bluman)
    J. Math. Phys. 37 (1996), 2361-2375.

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Symmetries, Exact Solutions, and Analysis of PDEs

  • Group-invariant solutions of semilinear Schrodinger equations in multi-dimensions.
    (with W. Feng)
    Accepted in J. Math. Phys. (2013).
  • Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions. (with S. Ali and T. Wolf)
    J. Math. Anal. Appl. 379 (2011), 748-763.
  • Exact solutions of nonlinear partial differential equations by the method of group foliation reduction.(with S. Ali and T. Wolf)
    SIGMA 7 (2011), 066 (10 pages).
  • Analytical properties and exact solutions of static plasma equilibrium systems
    in three dimensions. (with A. Cheviakov).
    Phys. Lett. A 372 (2008), 1363-1373.
  • Generalized symmetries of massless free fields on Minkowski space.
    (with J. Pohjanpelto)
    SIGMA 4 (2008), 004 (17 pages).
  • 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.

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Solitons

  • Travelling waves and conservation laws for complex mKdV-type equations.
    (with M. Mohuddin and T. Wolf)
    Appl. Math. Comput. 219 (2012) 679-698.
  • Interaction properties of complex mKdV solitons. (with N. Tchegoum Ngatat, M. Willoughby)
    Physica D 240 (2011) 1378-1394.

Integrable Systems and Curve Flows

  • Symplectically-invariant soliton equations from non-stretching geometric curve flows (with E. Asadi).
    J. Phys. A: Math. Theor. 45 (2012), 475207 (38 pages).
  • Integrable generalizations of Schrodinger maps and Heisenberg spin models
    from Hamiltonian flows of curves and surfaces. (with R. Myrzakulov)
    J. Geom. Phys. 60 (2010), 1576-1603.
  • Quaternion soliton equations from Hamiltonian curve flows in HP^n. (with E. Asadi)
    J. Phys. A: Math. Theor. 42 (2009), 485201 (25 pages).
  • Curve flows in Lagrange-Finsler geometry, bi-Hamiltonian structures
    and solitons. (with S. Vacaru)
    J. Geom. Phys. 59 (2009), 79-103.
  • Group-invariant soliton equations and bi-Hamiltonian geometric curve flows
    in Riemannian symmetric spaces.
    J. Geom. Phys. 58 (2008), 1-37.
  • Hamiltonian curve flows in Lie groups G\subsetU(N) and vector NLS, mKdV,
    sine-Gordon soliton equations.
    in IMA Volumes in Mathematics and its Applications, Vol. 144 (2007), 223-250.
  • Hamiltonian flows of curves in symmetric spaces G/SO(N) and vector soliton equations of mKdV and sine-Gordon type.
    SIGMA 2 (2006), 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.

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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.

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Field Equations and Mathematical Physics

  • Integrable generalizations of Schrodinger maps and Heisenberg spin models
    from Hamiltonian flows of curves and surfaces. (with R. Myrzakulov)
    J. Geom. Phys. 60 (2010), 1576-1603.
  • Generalized symmetries of massless free fields on Minkowski space.
    (with J. Pohjanpelto)
    SIGMA 4 (2008), 004 (17 pages).
  • Some Penrose transforms in complex differential geometry. (with J. Bland and M. Eastwood)
    Science in China Series A: Mathematics 49  (2006), 1599-1610.
  • 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 (2004), 1-12.
  • Conserved currents of massless spin s fields. (with J. Pohjanpelto)
    Proc. Roy. Soc. 459 (2003), 1215-1239.
  • Classification of local conservation laws of Maxwell's equations. (with J. Pohjanpelto)
    Acta. Appl. Math. 69 (2001), 285-327.
  • Global existence for wave maps with torsion. (with J. Isenberg)
    Comm. Partial Diff. Eqns. 25 (2000), 1669--702.
  • Nonlocal symmetries and conservation laws of Maxwell's equations. (with G. Bluman)
    J. Math. Phys. 38 (1997), 3508-3532.
  • Does there exist a sensible quantum theory of an algebra-valued scalar field? (with R.M. Wald)
    Phys. Rev. D 39 (1989), 2297-2307.

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General Relativity

  • Spinor derivation of quasilocal mean curvature mass in General Relativity.
    Inter. J. Theor. Phys. 47 (2008), 684-695.
  • 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.

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