2022

Athorne, C. (2022) Gauß–Manin from scratch: theme, variations and fantasia. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 478(2262), 20220217. (doi: 10.1098/rspa.2022.0217)

2020

Athorne, C. (2020) Equivariance and algebraic relations for curves. Journal of Geometry and Physics, 155, 103748. (doi: 10.1016/j.geomphys.2020.103748)

2019

Athorne, C. (2019) Equivariance in the Theory of Higher Genus ℘-Functions. In: Modern Treatment of Symmetries, Differential Equations and Applications (Symmetry 2019), Nakhon Ratchasima, Thailand, 14-18 Jan 2019, 020004. (doi: 10.1063/1.5125069)

Athorne, C. and Yilmaz, H. (2019) Twisted laplace maps. Journal of Physics A: Mathematical and Theoretical, 52(22), 225201. (doi: 10.1088/1751-8121/ab1926)

2018

Athorne, C. (2018) Laplace maps and constraints for a class of third order partial differential operators. Journal of Physics A: Mathematical and Theoretical, 51(8), 085205. (doi: 10.1088/1751-8121/aaa475)

Athorne, C. (2018) Fifty years of mathematical physics: selected works of Ludwig Fadeev. Contemporary Physics, 59(4), p. 421. (doi: 10.1080/00107514.2018.1538165)[Book Review]

Athorne, C. (2018) Fractals in probability and analysis. Contemporary Physics, 59(4), p. 429. (doi: 10.1080/00107514.2018.1559228)[Book Review]

2016

Athorne, C. (2016) Fundamental principles of classical mechanics: a geometrical perspective. Contemporary Physics, 57(2), pp. 238-241. (doi: 10.1080/00107514.2015.1048299)

Athorne, C. and Yilmaz, H. (2016) Invariants of hyperbolic partial differential operators. Journal of Physics A: Mathematical and Theoretical, 49(13), 135201. (doi: 10.1088/1751-8113/49/13/135201)

2015

Athorne, C. (2015) Special functions. In: Grinfeld, M. (ed.) Mathematical Tools for Physicists. Wiley-VCH, Verlag GmbH & Co. KGaA: Weinheim, Germany, pp. 239-289. ISBN 9783527411887

2012

England, M. and Athorne, C. (2012) Generalised elliptic functions. Central European Journal of Mathematics, 10(5), pp. 1655-1672. (doi: 10.2478/s11533-012-0083-x)

Athorne, C. and Yilmaz, H. (2012) Laplace invariants for general hyperbolic systems. Journal of Nonlinear Mathematical Physics, 19(3), pp. 391-410. (doi: 10.1142/S1402925112500246)

Athorne, C. (2012) On the equivariant algebraic Jacobian for curves of genus two. Journal of Geometry and Physics, 62(4), pp. 724-730. (doi: 10.1016/j.geomphys.2011.12.016)

England, M. and Athorne, C. (2012) Building Abelian functions with Baker-Hirota operators. Symmetry, Integrability and Geometry: Methods and Applications, 8(037), pp. 1-36. (doi: 10.3842/SIGMA.2012.037)

2011

Athorne, C. (2011) A generalization of Baker's quadratic formulae for hyperelliptic ℘-functions. Physics Letters A, 375(28-29), pp. 2689-2693. (doi: 10.1016/j.physleta.2011.05.056)

2009

Athorne, C. (2009) Applications of Transvectants. In: Silvestrov, S., Paal, E., Abramov, V. and Stolin, A. (eds.) Generalized Lie Theory in Mathematics, Physics and Beyond. Springer-Verlag: Berlin, pp. 29-37. ISBN 978-3-540-85331-2

2008

Athorne, C. (2008) Identities for hyperelliptic ℘-functions of genus one, two and three in covariant form. Journal of Physics A: Mathematical and Theoretical, 41(41), p. 5202. (doi: 10.1088/1751-8113/41/41/415202)

2006

Athorne, C. (2006) Algebraic Hirota maps. In: Faddeev, L.D., van Moerbeke, P. and Lambert, F. (eds.) Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete. Series: Mathematics, physics and chemistry (201). Springer: Dordrecht, The Netherlands, pp. 17-33. ISBN 9781402035012

2005

Athorne, C. (2005) A novel approcah to the theory of Pade approximants. Journal of Nonlinear Mathematical Physics, 12(Supple), pp. 15-27. (doi: 10.2991/jnmp.2005.12.s2.2)

2004

Athorne, C. (2004) The representation theory of Pade approximants. Journal of Physics A: Mathematical and General, 37(31), pp. 7699-7710. (doi: 10.1088/0305-4470/37/31/004)

Athorne, C., Eilbeck, J.C. and Enolskii, V.Z. (2004) A SL(2) covariant theory of genus 2 hyperelliptic functions. Mathematical Proceedings of the Cambridge Philosophical Society, 136(2), pp. 269-286. (doi: 10.1017/S030500410300728X)

2003

Athorne, C., Eilbeck, J.C. and Enolskii, V.Z. (2003) Identities for the classical genus two p function. Journal of Geometry and Physics, 48(2-3), pp. 354-368. (doi: 10.1016/S0393-0440(03)00048-2)

Athorne, C. (2003) Covariant hyperelliptic functions of genus two. Theoretical and Mathematical Physics, 137(1), pp. 1359-1366. (doi: 10.1023/A:1026088203139)

2002

Yilmaz, H. and Athorne, C. (2002) The geometrically invariant form of evolution equations. Journal of Physics A: Mathematical and General, 35(11), pp. 2619-2625. (doi: 10.1088/0305-4470/35/11/308)

2001

Athorne, C. (2001) On solving a class of unbalanced Ermakov-Pinney systems. Journal of Physics A: Mathematical and General, 34(42), L563-L566. (doi: 10.1088/0305-4470/34/42/101)

Athorne, C. (2001) Hirota derivatives and representation theory. Glasgow Mathematical Journal, 43(A), pp. 1-8. (doi: 10.1017/S0017089501000015)

2000

Athorne, C. (2000) Darboux maps andD-modules. Theoretical and Mathematical Physics, 122(2), pp. 135-139. (doi: 10.1007/BF02551191)

1999

Athorne, C. (1999) On the Lie symmetry algebra of a general ordinary differential equation. Journal of Physics A: Mathematical and General, 31(31), pp. 6605-6614. (doi: 10.1088/0305-4470/31/31/008)

Athorne, C. (1999) Algebraic invariants and generalized hirota derivatives. Physics Letters A, 256(1), pp. 20-24. (doi: 10.1016/S0375-9601(99)00202-9)

Athorne, C. (1999) Projective lifts and generalised Ermakov and Bernoulli systems. Journal of Mathematical Analysis and Applications, 233(2), pp. 552-563. (doi: 10.1006/jmaa.1999.6305)

1997

Athorne, C. (1997) Symmetries of linear ordinary differential equations. Journal of Physics A: Mathematical and General, 30(13), pp. 4639-4649. (doi: 10.1088/0305-4470/30/13/015)

1995

Athorne, C. (1995) A Toda system. Physics Letters A, 206(3-4), pp. 162-166. (doi: 10.1016/0375-9601(95)00643-H)

1994

Hartl, T. and Athorne, C. (1994) Solvable structures and hidden symmetries. Journal of Physics A: Mathematical and General, 27(10), pp. 3463-3474. (doi: 10.1088/0305-4470/27/10/022)

Articles

Athorne, C. (2022) Gauß–Manin from scratch: theme, variations and fantasia. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 478(2262), 20220217. (doi: 10.1098/rspa.2022.0217)

Athorne, C. (2020) Equivariance and algebraic relations for curves. Journal of Geometry and Physics, 155, 103748. (doi: 10.1016/j.geomphys.2020.103748)

Athorne, C. and Yilmaz, H. (2019) Twisted laplace maps. Journal of Physics A: Mathematical and Theoretical, 52(22), 225201. (doi: 10.1088/1751-8121/ab1926)

Athorne, C. (2018) Laplace maps and constraints for a class of third order partial differential operators. Journal of Physics A: Mathematical and Theoretical, 51(8), 085205. (doi: 10.1088/1751-8121/aaa475)

Athorne, C. (2016) Fundamental principles of classical mechanics: a geometrical perspective. Contemporary Physics, 57(2), pp. 238-241. (doi: 10.1080/00107514.2015.1048299)

Athorne, C. and Yilmaz, H. (2016) Invariants of hyperbolic partial differential operators. Journal of Physics A: Mathematical and Theoretical, 49(13), 135201. (doi: 10.1088/1751-8113/49/13/135201)

England, M. and Athorne, C. (2012) Generalised elliptic functions. Central European Journal of Mathematics, 10(5), pp. 1655-1672. (doi: 10.2478/s11533-012-0083-x)

Athorne, C. and Yilmaz, H. (2012) Laplace invariants for general hyperbolic systems. Journal of Nonlinear Mathematical Physics, 19(3), pp. 391-410. (doi: 10.1142/S1402925112500246)

Athorne, C. (2012) On the equivariant algebraic Jacobian for curves of genus two. Journal of Geometry and Physics, 62(4), pp. 724-730. (doi: 10.1016/j.geomphys.2011.12.016)

England, M. and Athorne, C. (2012) Building Abelian functions with Baker-Hirota operators. Symmetry, Integrability and Geometry: Methods and Applications, 8(037), pp. 1-36. (doi: 10.3842/SIGMA.2012.037)

Athorne, C. (2011) A generalization of Baker's quadratic formulae for hyperelliptic ℘-functions. Physics Letters A, 375(28-29), pp. 2689-2693. (doi: 10.1016/j.physleta.2011.05.056)

Athorne, C. (2008) Identities for hyperelliptic ℘-functions of genus one, two and three in covariant form. Journal of Physics A: Mathematical and Theoretical, 41(41), p. 5202. (doi: 10.1088/1751-8113/41/41/415202)

Athorne, C. (2005) A novel approcah to the theory of Pade approximants. Journal of Nonlinear Mathematical Physics, 12(Supple), pp. 15-27. (doi: 10.2991/jnmp.2005.12.s2.2)

Athorne, C. (2004) The representation theory of Pade approximants. Journal of Physics A: Mathematical and General, 37(31), pp. 7699-7710. (doi: 10.1088/0305-4470/37/31/004)

Athorne, C., Eilbeck, J.C. and Enolskii, V.Z. (2004) A SL(2) covariant theory of genus 2 hyperelliptic functions. Mathematical Proceedings of the Cambridge Philosophical Society, 136(2), pp. 269-286. (doi: 10.1017/S030500410300728X)

Athorne, C., Eilbeck, J.C. and Enolskii, V.Z. (2003) Identities for the classical genus two p function. Journal of Geometry and Physics, 48(2-3), pp. 354-368. (doi: 10.1016/S0393-0440(03)00048-2)

Athorne, C. (2003) Covariant hyperelliptic functions of genus two. Theoretical and Mathematical Physics, 137(1), pp. 1359-1366. (doi: 10.1023/A:1026088203139)

Yilmaz, H. and Athorne, C. (2002) The geometrically invariant form of evolution equations. Journal of Physics A: Mathematical and General, 35(11), pp. 2619-2625. (doi: 10.1088/0305-4470/35/11/308)

Athorne, C. (2001) On solving a class of unbalanced Ermakov-Pinney systems. Journal of Physics A: Mathematical and General, 34(42), L563-L566. (doi: 10.1088/0305-4470/34/42/101)

Athorne, C. (2001) Hirota derivatives and representation theory. Glasgow Mathematical Journal, 43(A), pp. 1-8. (doi: 10.1017/S0017089501000015)

Athorne, C. (2000) Darboux maps andD-modules. Theoretical and Mathematical Physics, 122(2), pp. 135-139. (doi: 10.1007/BF02551191)

Athorne, C. (1999) On the Lie symmetry algebra of a general ordinary differential equation. Journal of Physics A: Mathematical and General, 31(31), pp. 6605-6614. (doi: 10.1088/0305-4470/31/31/008)

Athorne, C. (1999) Algebraic invariants and generalized hirota derivatives. Physics Letters A, 256(1), pp. 20-24. (doi: 10.1016/S0375-9601(99)00202-9)

Athorne, C. (1999) Projective lifts and generalised Ermakov and Bernoulli systems. Journal of Mathematical Analysis and Applications, 233(2), pp. 552-563. (doi: 10.1006/jmaa.1999.6305)

Athorne, C. (1997) Symmetries of linear ordinary differential equations. Journal of Physics A: Mathematical and General, 30(13), pp. 4639-4649. (doi: 10.1088/0305-4470/30/13/015)

Athorne, C. (1995) A Toda system. Physics Letters A, 206(3-4), pp. 162-166. (doi: 10.1016/0375-9601(95)00643-H)

Hartl, T. and Athorne, C. (1994) Solvable structures and hidden symmetries. Journal of Physics A: Mathematical and General, 27(10), pp. 3463-3474. (doi: 10.1088/0305-4470/27/10/022)

Book Sections

Athorne, C. (2015) Special functions. In: Grinfeld, M. (ed.) Mathematical Tools for Physicists. Wiley-VCH, Verlag GmbH & Co. KGaA: Weinheim, Germany, pp. 239-289. ISBN 9783527411887

Athorne, C. (2009) Applications of Transvectants. In: Silvestrov, S., Paal, E., Abramov, V. and Stolin, A. (eds.) Generalized Lie Theory in Mathematics, Physics and Beyond. Springer-Verlag: Berlin, pp. 29-37. ISBN 978-3-540-85331-2

Athorne, C. (2006) Algebraic Hirota maps. In: Faddeev, L.D., van Moerbeke, P. and Lambert, F. (eds.) Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete. Series: Mathematics, physics and chemistry (201). Springer: Dordrecht, The Netherlands, pp. 17-33. ISBN 9781402035012

Book Reviews

Athorne, C. (2018) Fifty years of mathematical physics: selected works of Ludwig Fadeev. Contemporary Physics, 59(4), p. 421. (doi: 10.1080/00107514.2018.1538165)[Book Review]

Athorne, C. (2018) Fractals in probability and analysis. Contemporary Physics, 59(4), p. 429. (doi: 10.1080/00107514.2018.1559228)[Book Review]

Conference Proceedings

Athorne, C. (2019) Equivariance in the Theory of Higher Genus ℘-Functions. In: Modern Treatment of Symmetries, Differential Equations and Applications (Symmetry 2019), Nakhon Ratchasima, Thailand, 14-18 Jan 2019, 020004. (doi: 10.1063/1.5125069)