Published on *Brock University* (http://www.brocku.ca)

- Conserved Integrals/Conservation Laws of PDEs
- Symmetries, Exact Solutions, and Analysis of PDEs
- Solitons
- Integrable Systems and Curve Flows
- Classical Gauge Theory
- Field Equations and Mathematical Physics
- General Relativity
- Publications Listed Chronologically

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.

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.

- 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.

- 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.

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.

- 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.

Main heading:

Department of Mathematics & Statistics