Publications



Published papers and manuscripts
accepted for publication


  • R.G. Halburd, R.J. Korhonen and K. Tohge, Holomorphic curves with shift-invariant hyperplane preimages, Transactions of the American Mathematical Society. Published online, 24 March 2014.

  • R.G. Halburd and T. Kecker, Local and global finite branching of solutions of ordinary differential equations. To appear in the Proceedings of the Workshop Honoring Ilpo Laine's Seventieth Birthday. Reports and Studies in Forestry and Natural Sciences. 14 (2014)

  • R.G. Halburd and R.J. Korhonen, Value distribution and linear operators, Proceedings of the Edinburgh Mathematical Society. Published online, 22 November 2013.

  • R.G. Halburd and R.J. Korhonen, Non-decreasing functions, exceptional sets and generalised Borel lemmas, J. Aust. Math. Soc. 88: 353-361 (2010)

  • B. Grammaticos, R.G. Halburd, A. Ramani and C.-M Viallet, How to detect the integrability of discrete systems (topical review), J. Phys. A:Math. Theor. 42 454002 (2009)

  • G. Filipuk and R.G. Halburd, Rational ODEs with movable algebraic singularities, Studies in Applied Mathematics 123: 17-36 (2009)

  • R.G. Halburd and N.J. Southall, Tropical Nevanlinna theory and ultradiscrete equations, International Mathematics Research Notices 2009: 887-91 (2009)

  • G. Filipuk and R.G. Halburd, Movable singularities of equations of Liénard type Computational Methods and Function Theory 9: 551-563 (2009)

  • G. Filipuk and R.G. Halburd, Movable algebraic singularities of second-order ordinary differential equations, J. Math. Phys. 50, 023509 (2009)

  • R.G. Halburd, Book Review of 'Partial Differential Equations in General Relativity', J. Phys. A:Math. Theor. 41 479003 (2008)
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  • R.G. Halburd and R.J. Korhonen, Meromorphic solutions of difference equations, integrability and the discrete Painlevé equations (topical review), J. Phys. A. 40:R1-R38, (2007)
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  • J.B. Griffiths and R. Halburd, The C-metric as a colliding plane wave spacetime, Class. Quantum Grav. 24: 1049-1054 (2007)
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  • R.G. Halburd and R.J. Korhonen, Finite-order meromorphic solutions and the discrete Painlevé equations, Proc. London Math. Soc.  94: 443-474 (2007)
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  • D.C. Barnett, R.G. Halburd, R.J. Korhonen, and W. Morgan, Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations, Proc. Roy. Soc. Edinburgh, Sect. A. 137: 457-474 (2007)
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  • R.G. Halburd and R.J. Korhonen, Existence of finite-order meromorphic solutions as a detector of integrability in difference equations, Phys. D 218: 191--203 (2006)
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  • R.G. Halburd and R.J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math. 31: 463--478 (2006)
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  • R.G. Halburd and R.J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314:477-487 (2006)
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  • R.G. Halburd Diophantine integrability, J. Phys. A. 38: L263-L269 (2005)
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  • M.J. Ablowitz, S. Chakravarty, and R.G. Halburd, Integrable systems and reductions of the self-dual Yang-Mills equations, J. Math. Phys. 44: 3147-3173 (2003)
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  • Y.M. Chiang, and R.G. Halburd, On the meromorphic solutions of an equation of Hayman, J. Math. Anal. Appl. 281: 663-677 (2003)
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  • S. Chakravarty, and R.G. Halburd, First integrals of a generalized Darboux-Halphen system, J. Math. Phys. 44: 1751-1762 (2003)
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  • S. Chakravarty, R.G. Halburd, and S.L. Kent, Self-similar solutions of certain coupled integrable systems, J. Phys. A. 36: 1371-1384 (2003)
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  • S. Chakravarty, and R. Halburd, First integrals and gradient flow for a generalized Darboux-Halphen system in the legacy of the inverse scattering transform in applied mathematics (South Hadley, MA, 2001), Contemp. Math.  301: 273-281 (2002)
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  • R. Halburd, Shear-free Relativistic fluids and the absence of movable branch Points, J. Math. Phys. 43: 1966-1979 (2002)
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  • R. Halburd, Solvable models of relativistic charged spherically symmetric fluids, Class. Quantum Grav. 18:11-25 (2001)
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  • M.J. Ablowitz and R. Halburd, Nevanlinna theory and difference equations of Painlevé type, Proceedings of the Workshop on Nonlinearity, Integrability and All That: Twenty Years after NEEDS '79 (Gallipoli, 1999), 3-11, World Sci. Publishing, River Edge, NJ, 2000
    PDF (116 KB) or Postscript (112 KB)

  • M.J. Ablowitz, R. Halburd, and B. Herbst, On the extension of the Painlevé property to difference equations, Nonlinearity, 13: 889-905 (2000)
    PDF (116 KB) or Postscript (460 KB)

  • M.J. Ablowitz, S. Chakravarty, and R. Halburd, The generalized Chazy equation from the self-duality equations, Stud. Appl. Math. 103: 75-88 (1999)
    PDF (148 KB) or Postscript (160 KB)

  • R. Halburd, Integrable relativistic models and the generalized Chazy equation, Nonlinearity, 12, 931-938 (1999)
    PDF (68 KB) or Postscript (264 KB)

  • M.J. Ablowitz, S. Chakravarty, and R. Halburd, The generalized Chazy equation and Schwarzian triangle functions, Asian J. Math., 2: 619-624 (1999)
    PDF (108 KB) or Postscript (104 KB)

  • M.J. Ablowitz, S. Chakravarty, and R. Halburd, The Darboux-Halphen system and the singularity structure of its solutions, in Proc. Fourth Int. Conf. on Mathematical and Numerical Aspects of Wave Propagation, J.A. DeSanto ed, SIAM, Philadelphia, 408-412 (1998)
    MR reference 1 635 372
    PDF (108 KB) or Postscript (88 KB)

  • M.J. Ablowitz, S. Chakravarty, and R. Halburd, On Painlevé and Darboux-Halphen type equations, in the Painlevé property, one century later, CRM series in mathematical physics, Springer, New York, ed. R. Conte, 573-590 (1999)
    PDF (184 KB) or Postscript (208 KB)

  • M.D. Kruskal, N. Joshi, and R. Halburd, Analytic and asymptotic methods for nonlinear singularity analysis: a review and extensions of tests for the Painlevé property, Integrability of Nonlinear Systems (Pondicherry, India, 1996). Eds B. Grammaticos and K. Tamizhmani, Lecture Notes in Physics 495: 171-205, Springer, Berlin (1997)
    MR reference 1 636 294
    PDF (284 KB) or Postscript (944 KB)

  • R. Halburd and N. Joshi, The coalescence limit of the second Painlevé equation, Stud. Appl. Math., 97: 1-15, (1996)
    MR reference 97c:34055
    PDF (164 KB) or Postscript (184 KB)

  • R. Halburd, Symmetries of the self-dual Yang-Mills equations, Bull. Austral. Math. Soc., 49: 151-158, (1994).
    MR reference 95c:53031

  • N. Joshi, D. Burtonclay, and R.G. Halburd, Nonlinear nonautonomous discrete dynamical systems from a general discrete isomonodromy problem, Lett. Math. Phys., 26: 123-131, (1992).
    MR reference 94f:58060

Manuscripts submitted for publication

  • A. Al-Ghassani and R.G. Halburd, Height growth and a discrete Painlevé equation. Submitted.

  • R.G. Halburd and J. Wang, All admissible meromorphic solutions of Hayman's equation. Submitted.