Dr J. Gibbons

    Postgraduate Tutor, Mathematics Department

    • Room No : 622, Huxley Building
    • Telephone No. : +44 207 594 8506
    • E-Mail Address : j.gibbons@ic.ac.uk

    Research Interests :

    • General Research interests: Integrable classical mechanics; Applied mathematics.

    • Particular Research Interests:
        • Hamiltonian dynamics. Integrable systems.
        Benney's equations, the Zabolotskaya-Khokhlov equation. Systems of hydrodynamic type.
        Reductions of the Benney equations, their geometrical properties, and construction of explicit examples using algebro-geometric methods.

    See the Integrable Systems Group website.

    Courses given this year (2005-6)

    • M3M3 Partial Differential Equations - solution sheet 3
    • M2A2 Lagrangian Mechanics - course notes
    • ME2.6 2nd year maths for Mechanical Engineering - syllabus , handouts etc.

      • Some Recent Publications :

    • Solving Dispersionless Lax Equations, J.Gibbons, Y.Kodama, Proceedings of NATO ASI, 'Singular Limits of Dispersive Waves' ed. N.Ercolani, Plenum 1994.
    • Reductions of the Benney Equations, J.Gibbons, S.P.Tsarev, Physics Letters 211A, (1996), 19.
    • Conformal maps and reductions of the Benney equations, J. Gibbons, S.P. Tsarev, Physics Letters 258A,(1999), 263-271.
    • The initial value problem for reductions of the Benney equations, J. Gibbons, L.A. Yu, Inverse Problems 16 No 3 (June 2000) 605-618 .
    • Hyperelliptic reduction of the Benney moment equations, S Baldwin and J Gibbons, J. Phys. A: Math. Gen. 36 No 31 (8 August 2003) 8393-8417
    • Higher genus hyperelliptic reductions of the Benney equations, Sadie Baldwin and John Gibbons, J. Phys. A: Math. Gen. 37 No 20 (21 May 2004) 5341-5354 }
    • Genus 4 trigonal reduction of the Benney equations, Sadie Baldwin and John Gibbons, J. Phys. A: Math. Gen. 39 No 14 (7 April 2006) 3607-3639
    • Addition theorems on the strata of the theta divisor of genus 3 hyperelliptic curves, Victor Enolski and John Gibbons, in preparation.

      • My current PhD student is:

      • Andrea Raimondo (1st year).

        • Past and current collaborators include:

        • Allan Fordy, Leeds
        • Boris Kupershmidt, Tennessee
        • Darryl Holm, Imperial and Los Alamos
        • Yuji Kodama, Ohio and Osaka
        • Serguei Tsarev, Krasnoyarsk
        • Victor Enolski, Kiev

        Other interests:

        • Traditional music of Northumberland, Ireland and elsewhere, on Northumbrian smallpipes, Border pipes, flute and tin whistle.


        If you would like to contact me about my research or teaching, my email address is j.gibbons@ic.ac.uk. However, emails about postgraduate matters should go to mathspgadmit@ic.ac.uk.

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