2022

Gilson, C. R. (2022) A visual approach to the ultradiscrete KdV equation with non-integer site values. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 478(2262), 20220150. (doi: 10.1098/rspa.2022.0150)

2020

Gilson, C. R. , Hamanaka, M., Huang, S.-C. and Nimmo, J. J.C. (2020) Soliton solutions of noncommutative anti-self-dual Yang-Mills equations. Journal of Physics A: Mathematical and Theoretical, 53(40), 404002. (doi: 10.1088/1751-8121/aba72e)

2019

Nimmo, J. J.C., Gilson, C. R. and Willox, R. (2019) Darboux dressing and undressing for the ultradiscrete KdV equation. Journal of Physics A: Mathematical and Theoretical, 52(44), 445201. (doi: 10.1088/1751-8121/ab45cf)

2018

Barnett, S. M. , Ferenczi, G., Gilson, C. R. and Speirits, F. C. (2018) Statistics of photon-subtracted and photon-added states. Physical Review A: Atomic, Molecular and Optical Physics, 98(1), 013809. (doi: 10.1103/PhysRevA.98.013809)

2016

Barnett, S. M. , Allen, L., Cameron, R. P., Gilson, C. R. , Padgett, M. J. , Speirits, F. C. and Yao, A. M. (2016) On the natures of the spin and orbital parts of optical angular momentum. Journal of Optics, 18(6), 064004. (doi: 10.1088/2040-8978/18/6/064004)

2015

Cameron, R. P., Speirits, F. C. , Gilson, C. R. , Allen, L. and Barnett, S. M. (2015) The azimuthal component of Poynting's vector and the angular momentum of light. Journal of Optics, 17(12), 125610. (doi: 10.1088/2040-8978/17/12/125610)

Gilson, C.R. , Nimmo, J.J.C. and Nagai, A. (2015) A direct approach to the ultradiscrete KdV equation with negative. Journal of Physics A: Mathematical and General, 48(29), 295201. (doi: 10.1088/1751-8113/48/29/295201)

2009

Gilson, C.R., Hamanaka, M. and Nimmo, J.J.C. (2009) Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations. Glasgow Mathematical Journal, 51(A), pp. 83-93. (doi: 10.1017/S0017089508004801)

Gilson, C. R. , Hamanaka, M. and Nimmo, J. J. C. (2009) Backlund transformations and the Atiyah-Ward ansatz for non-commutative anti-self-dual Yang-Mills equations. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 465(2108), pp. 2613-2632. (doi: 10.1098/rspa.2008.0515)

Gilson, C.R. and Macfarlane, S.R. (2009) Dromion solutions of noncommutative Davey–Stewartson equations. Journal of Physics A: Mathematical and Theoretical, 42(23), p. 235202. (doi: 10.1088/1751-8113/42/23/235202)

2008

Gilson, C.R., Nimmo, J.J.C. and Sooman, C.M. (2008) On a direct approach to quasideterminant solutions of a noncommutative modified KP equation. Journal of Physics A: Mathematical and Theoretical, 41(8), 085202. (doi: 10.1088/1751-8113/41/8/085202)

2007

Gilson, C.R., Nimmo, J.J.C. and Ohta, Y. (2007) Quasideterminant solutions of a non-Abelian Hirota-Miwa equation. Journal of Physics A: Mathematical and Theoretical, 40(42), pp. 12607-12617. (doi: 10.1088/1751-8113/40/42/S07)

Gilson, C.R. and Nimmo, J.J.C. (2007) On a direct approach to quasideterminant solutions of a noncommutative KP equation. Journal of Physics A: Mathematical and Theoretical, 40(14), pp. 3839-3850. (doi: 10.1088/1751-8113/40/14/007)

2006

Croke, S. , Andersson, E., Barnett, S.M. , Gilson, C.R. and Jeffers, J. (2006) Maximum confidence quantum measurements. Physical Review Letters, 96(7), 070401. (doi: 10.1103/PhysRevLett.96.070401)

2005

Gilson, C.R. and Nimmo, J.J.C. (2005) The relation between a 2D Lotka-Volterra equation and a 2D Toda lattice. Journal of Nonlinear Mathematical Physics, 12(Supple), pp. 169-179. (doi: 10.2991/jnmp.2005.12.s2.12)

2003

Gilson, C., Hietarinta, J., Nimmo, J.J.C. and Ohta, Y. (2003) Sasa-Satsuma higher-order nonlinear Schrodinger equation and its bilinearization and multisoliton solutions. Physical Review E, 68(1), 016614. (doi: 10.1103/PhysRevE.68.016614)

Hunter, K., Andersson, E., Gilson, C.R. and Barnett, S.M. (2003) Maximum fidelity for a mirror symmetric set of qubit states. Journal of Physics A: Mathematical and General, 36(14), pp. 4159-4172. (doi: 10.1088/0305-4470/36/14/317)

Gilson, C.R., Hu, X.-B., Ma, W.-X. and Tam, H.-W. (2003) Two integrable differential-difference equations derived from the discrete BKP equation and their related equations. Physica D: Nonlinear Phenomena, 175(3-4), pp. 177-184. (doi: 10.1016/S0167-2789(02)00736-4)

2002

Gilson, C.R. (2002) Generalizing the KP hierarchies: Pfaffian hierarchies. Theoretical and Mathematical Physics, 133(3), pp. 1663-1674. (doi: 10.1023/A:1021314325242)

Gilson, C.R., Hu, X.-B. and Barnett, S.M. (2002) On multiple soliton solutions of some simple differential-difference equations. Inverse Problems, 18(6), pp. 1499-1508. (doi: 10.1088/0266-5611/18/6/304)

Andersson, E., Barnett, S.M., Gilson, C.R. and Hunter, K. (2002) Minimum-error discrimination between three mirror-symmetric states. Physical Review A: Atomic, Molecular and Optical Physics, 65(5), 052308. (doi: 10.1103/PhysRevA.65.052308)

2001

Gilson, C.R., Nimmo, J.J.C. and Tsujimoto, S. (2001) Pfaffianization of the discrete KP equation. Journal of Physics A: Mathematical and General, 34(48), pp. 10569-10575. (doi: 10.1088/0305-4470/34/48/320)

Barnett, S.M., Gilson, C.R. and Sasaki, M. (2001) Fidelity and the communication of quantum information. Journal of Physics A: Mathematical and General, 34(35), pp. 6755-6766. (doi: 10.1088/0305-4470/34/35/303)

Gilson, C.R. and Nimmo, J.J.C. (2001) Pfaffianization of the Davey-Stewartson equations. Theoretical and Mathematical Physics, 128(1), pp. 870-882.

Ohta, Y., Nimmo, J.J.C. and Gilson, C.R. (2001) A bilinear approach to a Pfaffian self-dual Yang-Mills equation. Glasgow Mathematical Journal, 43(A), pp. 99-108. (doi: 10.1017/S001708950100009X)

Articles

Gilson, C. R. (2022) A visual approach to the ultradiscrete KdV equation with non-integer site values. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 478(2262), 20220150. (doi: 10.1098/rspa.2022.0150)

Gilson, C. R. , Hamanaka, M., Huang, S.-C. and Nimmo, J. J.C. (2020) Soliton solutions of noncommutative anti-self-dual Yang-Mills equations. Journal of Physics A: Mathematical and Theoretical, 53(40), 404002. (doi: 10.1088/1751-8121/aba72e)

Nimmo, J. J.C., Gilson, C. R. and Willox, R. (2019) Darboux dressing and undressing for the ultradiscrete KdV equation. Journal of Physics A: Mathematical and Theoretical, 52(44), 445201. (doi: 10.1088/1751-8121/ab45cf)

Barnett, S. M. , Ferenczi, G., Gilson, C. R. and Speirits, F. C. (2018) Statistics of photon-subtracted and photon-added states. Physical Review A: Atomic, Molecular and Optical Physics, 98(1), 013809. (doi: 10.1103/PhysRevA.98.013809)

Barnett, S. M. , Allen, L., Cameron, R. P., Gilson, C. R. , Padgett, M. J. , Speirits, F. C. and Yao, A. M. (2016) On the natures of the spin and orbital parts of optical angular momentum. Journal of Optics, 18(6), 064004. (doi: 10.1088/2040-8978/18/6/064004)

Cameron, R. P., Speirits, F. C. , Gilson, C. R. , Allen, L. and Barnett, S. M. (2015) The azimuthal component of Poynting's vector and the angular momentum of light. Journal of Optics, 17(12), 125610. (doi: 10.1088/2040-8978/17/12/125610)

Gilson, C.R. , Nimmo, J.J.C. and Nagai, A. (2015) A direct approach to the ultradiscrete KdV equation with negative. Journal of Physics A: Mathematical and General, 48(29), 295201. (doi: 10.1088/1751-8113/48/29/295201)

Gilson, C.R., Hamanaka, M. and Nimmo, J.J.C. (2009) Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations. Glasgow Mathematical Journal, 51(A), pp. 83-93. (doi: 10.1017/S0017089508004801)

Gilson, C. R. , Hamanaka, M. and Nimmo, J. J. C. (2009) Backlund transformations and the Atiyah-Ward ansatz for non-commutative anti-self-dual Yang-Mills equations. Proceedings of the Royal Society of London Series A: Mathematical, Physical and Engineering Sciences, 465(2108), pp. 2613-2632. (doi: 10.1098/rspa.2008.0515)

Gilson, C.R. and Macfarlane, S.R. (2009) Dromion solutions of noncommutative Davey–Stewartson equations. Journal of Physics A: Mathematical and Theoretical, 42(23), p. 235202. (doi: 10.1088/1751-8113/42/23/235202)

Gilson, C.R., Nimmo, J.J.C. and Sooman, C.M. (2008) On a direct approach to quasideterminant solutions of a noncommutative modified KP equation. Journal of Physics A: Mathematical and Theoretical, 41(8), 085202. (doi: 10.1088/1751-8113/41/8/085202)

Gilson, C.R., Nimmo, J.J.C. and Ohta, Y. (2007) Quasideterminant solutions of a non-Abelian Hirota-Miwa equation. Journal of Physics A: Mathematical and Theoretical, 40(42), pp. 12607-12617. (doi: 10.1088/1751-8113/40/42/S07)

Gilson, C.R. and Nimmo, J.J.C. (2007) On a direct approach to quasideterminant solutions of a noncommutative KP equation. Journal of Physics A: Mathematical and Theoretical, 40(14), pp. 3839-3850. (doi: 10.1088/1751-8113/40/14/007)

Croke, S. , Andersson, E., Barnett, S.M. , Gilson, C.R. and Jeffers, J. (2006) Maximum confidence quantum measurements. Physical Review Letters, 96(7), 070401. (doi: 10.1103/PhysRevLett.96.070401)

Gilson, C.R. and Nimmo, J.J.C. (2005) The relation between a 2D Lotka-Volterra equation and a 2D Toda lattice. Journal of Nonlinear Mathematical Physics, 12(Supple), pp. 169-179. (doi: 10.2991/jnmp.2005.12.s2.12)

Gilson, C., Hietarinta, J., Nimmo, J.J.C. and Ohta, Y. (2003) Sasa-Satsuma higher-order nonlinear Schrodinger equation and its bilinearization and multisoliton solutions. Physical Review E, 68(1), 016614. (doi: 10.1103/PhysRevE.68.016614)

Hunter, K., Andersson, E., Gilson, C.R. and Barnett, S.M. (2003) Maximum fidelity for a mirror symmetric set of qubit states. Journal of Physics A: Mathematical and General, 36(14), pp. 4159-4172. (doi: 10.1088/0305-4470/36/14/317)

Gilson, C.R., Hu, X.-B., Ma, W.-X. and Tam, H.-W. (2003) Two integrable differential-difference equations derived from the discrete BKP equation and their related equations. Physica D: Nonlinear Phenomena, 175(3-4), pp. 177-184. (doi: 10.1016/S0167-2789(02)00736-4)

Gilson, C.R. (2002) Generalizing the KP hierarchies: Pfaffian hierarchies. Theoretical and Mathematical Physics, 133(3), pp. 1663-1674. (doi: 10.1023/A:1021314325242)

Gilson, C.R., Hu, X.-B. and Barnett, S.M. (2002) On multiple soliton solutions of some simple differential-difference equations. Inverse Problems, 18(6), pp. 1499-1508. (doi: 10.1088/0266-5611/18/6/304)

Andersson, E., Barnett, S.M., Gilson, C.R. and Hunter, K. (2002) Minimum-error discrimination between three mirror-symmetric states. Physical Review A: Atomic, Molecular and Optical Physics, 65(5), 052308. (doi: 10.1103/PhysRevA.65.052308)

Gilson, C.R., Nimmo, J.J.C. and Tsujimoto, S. (2001) Pfaffianization of the discrete KP equation. Journal of Physics A: Mathematical and General, 34(48), pp. 10569-10575. (doi: 10.1088/0305-4470/34/48/320)

Barnett, S.M., Gilson, C.R. and Sasaki, M. (2001) Fidelity and the communication of quantum information. Journal of Physics A: Mathematical and General, 34(35), pp. 6755-6766. (doi: 10.1088/0305-4470/34/35/303)

Gilson, C.R. and Nimmo, J.J.C. (2001) Pfaffianization of the Davey-Stewartson equations. Theoretical and Mathematical Physics, 128(1), pp. 870-882.

Ohta, Y., Nimmo, J.J.C. and Gilson, C.R. (2001) A bilinear approach to a Pfaffian self-dual Yang-Mills equation. Glasgow Mathematical Journal, 43(A), pp. 99-108. (doi: 10.1017/S001708950100009X)