Publications
25 results found
Gibbons J, Matsutani S, Onishi Y, 2013, Relationship between the prime form and the sigma function for some cyclic (<i>r</i>, <i>s</i>) curves, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 46, ISSN: 1751-8113
- Author Web Link
- Cite
- Citations: 1
Gibbons J, 2011, Constructing Benney Reductions associated with cyclic (n,s) Curves., Computational Methods and Function Theory, Vol: 11, Pages: 671-684, ISSN: 1617-9447
Benney's equations admit 'reductions' to systems of dispersionless pdes with only finitely many N dependent variables. These reductions are parametrisedby conformal mappings from the half-plane to the half-plane minus N slits.A large family of these can be constructed as Schwartz-Christoffel mappings;an important subclass of these reduce to integrals of a second kind differential on an algebraic curve. Particular examples of these have beenconstructed; in particular there are 2 different constructions for the caseof a hyperelliptic curve. Other particular examples have been worked out,and the overall structure is similar to the hyperelliptic case, though thereare differences of detail. It is thus important to find the general structureof these, independently of the particular curve being studied. We use theFay Prime Form to investigate this, and sketch how this approach could be applied to general cyclic (n,s) curves.
Eilbeck JC, Enolski VZ, Gibbons J, 2010, Sigma, tau and Abelian functions of algebraic curves, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 43, ISSN: 1751-8113
- Author Web Link
- Cite
- Citations: 12
Gibbons J, Lorenzoni P, Raimondo A, 2010, Purely nonlocal Hamiltonian formalism for systems of hydrodynamic type, JOURNAL OF GEOMETRY AND PHYSICS, Vol: 60, Pages: 1112-1126, ISSN: 0393-0440
- Author Web Link
- Cite
- Citations: 3
England M, Gibbons J, 2009, A genus six cyclic tetragonal reduction of the Benney equations, JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, Vol: 42, ISSN: 1751-8113
- Author Web Link
- Cite
- Citations: 17
Gibbons J, Lorenzoni P, Raimondo A, 2009, Hamiltonian Structures of Reductions of the Benney System, COMMUNICATIONS IN MATHEMATICAL PHYSICS, Vol: 287, Pages: 291-322, ISSN: 0010-3616
- Author Web Link
- Cite
- Citations: 8
Gibbons J, Veselov AP, 2009, On the rational monodromy-free potentials with sextic growth, JOURNAL OF MATHEMATICAL PHYSICS, Vol: 50, ISSN: 0022-2488
- Author Web Link
- Cite
- Citations: 21
Gibbons J, Holm DD, Tronci C, 2008, Geometry of Vlasov kinetic moments: A bosonic Fock space for the symmetric Schouten bracket, PHYSICS LETTERS A, Vol: 372, Pages: 4184-4196, ISSN: 0375-9601
- Author Web Link
- Cite
- Citations: 19
Baldwin S, Eilbeck JC, Gibbons J, et al., 2008, Abelian functions for cyclic trigonal curves of genus 4, JOURNAL OF GEOMETRY AND PHYSICS, Vol: 58, Pages: 450-467, ISSN: 0393-0440
- Author Web Link
- Cite
- Citations: 34
Holm D, Gibbons J, Tronci C, 2007, Vlasov moments, integrable systems and singular solutions, Physics Letters A
Gibbons J, Raimondo A, 2007, Differential geometry of hydrodynamic Vlasov equations, Journal of Geometry and Physics, Vol: 57, Pages: 1815-1828, ISSN: 0393-0440
Baldwin S, Gibbons J, 2006, Genus 4 trigonal reduction of the Benney equations, Journal of Physics -London- A Mathematical and General, Vol: 39, Pages: 3607-3640, ISSN: 0305-4470
Baldwin S, Gibbons J, 2004, Higher genus hyperelliptic reductions of the Benney equations, Journal of Physics A - Mathematical and General, Vol: 37, Pages: 5341-5354, ISSN: 0305-4470
Baldwin S, Gibbons J, 2003, Hyperelliptic reduction of the Benney moment equations, JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, Vol: 36, Pages: 8393-8417, ISSN: 0305-4470
- Author Web Link
- Open Access Link
- Cite
- Citations: 15
Baker SM, Elgin JN, Gibbons J, 2000, Polarization dynamics of solitons in birefringent fibers, Physical Review E-Statistical physics, plasmas, fluids, and related interdisciplinary topics, Vol: 62, Pages: 4325-4332, ISSN: 1063-651X
Yu L, Gibbons J, 2000, The initial value problem for reductions of the Benney equations, Inverse Problems, Vol: 16, Pages: 605-618, ISSN: 0266-5611
Baker SM, Elgin JN, Gibbons J, 2000, Polarization dynamics of solitons in birefringent fibers, Physical Review E-Statistical physics, plasmas, fluids, and related interdisciplinary topics, Vol: 62, Pages: 4325-4332, ISSN: 1063-651X
Gibbons J, Tsarev SP, 1999, Conformal maps and reductions of the Benney equations, Physics Letters A, Vol: 258, Pages: 263-271, ISSN: 0375-9601
Gibbon JD, Gibbons J, Heritage M, 1997, A logarithmic 3d Euler inequality, PHYSICS OF FLUIDS, Vol: 9, Pages: 471-472, ISSN: 1070-6631
Gibbons J, Tsarev SP, 1996, Reductions of the Benney equations, Physics Letters A, Vol: 211, Pages: 19-24, ISSN: 0375-9601
GIBBONS J, KODAMA Y, 1994, SOLVING DISPERSIONLESS LAX EQUATIONS, NATO Advanced Research Workshop, and a Chaos, Order, and Pattern Panel Sponsored Workshop on Singular Limits of Dispersive Waves, Publisher: PLENUM PRESS DIV PLENUM PUBLISHING CORP, Pages: 61-66, ISSN: 0258-1221
- Author Web Link
- Cite
- Citations: 19
GIBBONS J, KUPERSHMIDT BA, 1992, TIME DISCRETIZATIONS OF LATTICE INTEGRABLE SYSTEMS, PHYSICS LETTERS A, Vol: 165, Pages: 105-110, ISSN: 0375-9601
- Author Web Link
- Cite
- Citations: 9
GIBBONS J, KUPERSHMIDT BA, 1990, CONNECTIONS BETWEEN FREE-SURFACE SYSTEMS OF HYDRODYNAMICAL TYPE AND GENERALIZED KINETIC-EQUATIONS, PHYSICS LETTERS A, Vol: 144, Pages: 211-219, ISSN: 0375-9601
GIBBONS J, KUPERSHMIDT BA, 1989, KINETIC REPRESENTATION OF THE KP HIERARCHY, PHYSICS LETTERS A, Vol: 139, Pages: 141-145, ISSN: 0375-9601
- Author Web Link
- Cite
- Citations: 1
GIBBONS J, KUPERSHMIDT BA, 1989, KINETIC REPRESENTATION OF DISCRETE INTEGRABLE SYSTEMS, JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, Vol: 22, Pages: L559-L561, ISSN: 0305-4470
This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.