- Room No :
**622, Huxley Building** - Telephone No. :
**+44 207 594 8506** - E-Mail Address :
**j.gibbons@ic.ac.uk** - General Research interests: Integrable classical mechanics; Applied mathematics.
- Particular Research Interests:
- M3M3 Partial Differential Equations - solution sheet 3
- M2A2 Lagrangian Mechanics - course notes
- ME2.6 2nd year maths for Mechanical Engineering - syllabus , handouts etc.
- 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.
- Andrea Raimondo (1st year).
- Allan Fordy, Leeds
- Boris Kupershmidt, Tennessee
- Darryl Holm, Imperial and Los Alamos
- Yuji Kodama, Ohio and Osaka
- Serguei Tsarev, Krasnoyarsk
- Victor Enolski, Kiev
- Traditional music of Northumberland, Ireland and elsewhere, on Northumbrian smallpipes, Border pipes, flute and tin whistle.

- 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.

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.