Dr Mark Jones


I was educated at University College London where I graduated with a Bachelor of Science in Mathematics. I then moved to the University of Bath where I wrote my doctoral thesis entitled 'The Bifurcation and Secondary Bifurcation of Capillary-Gravity waves in the presence of symmetry' under the supervision of Professor JF Toland FRS. I then moved to the Queens University of Belfast and subsequently joined Kingston in 2000.

Academic responsibilities

Senior lecturer


  • BSc
  • PhD


My research is mostly concerned with  the mathematical study of water waves. My early research work was quite pure mathematical in nature, consisting of a study of the waves which may bifurcate from the line of trivial solutions when the solution space of the underlying linearized model equation is two dimensional.  I have returned to aspect of this problem throughout my career, generalising it to  interfacial waves.

The other strand of my research involves a study of the stability of these waves. I have employed the method of multiple scales to show how they may be modelled by a pair of coupled nonlinear partial differential equations  for the wave amplitudes. These equations can then be used to determine the stability properties of the waves.


Jump to: Article
Number of items: 28.


Jones, M.C.W. (2021) Double degeneracy in the immiscible Wilton ripple phenomenon : a three perturbation parameter problem in bifurcation theory. International Journal of Bifurcation and Chaos, 31(13), p. 2150190. ISSN (print) 0218-1274

Jones, Mark and Hunter, Gordon (2019) Conservation laws for a non-linear system describing the propagation of "triadic" waves. Proceedings of the Institute of Acoustics, 41(1), pp. 137-145. ISSN (print) 1478-6095

Jones, M.C.W. (2018) Resonant interfacial capillary-gravity waves in the presence of damping effects. European Journal of Mechanics - B/Fluids, 68, pp. 20-29. ISSN (print) 0997-7546

Jones, Mark (2017) A singularity in resonant interfacial fluid flow leading to role reversal in the space time continuum of the evolution equations. Wave Motion, 75, pp. 77-87. ISSN (print) 0165-2125

Jones, M.C.W. (2016) Soliton solutions to coupled nonlinear evolution equations modelling a third harmonic resonance in the theory of capillary-gravity waves. Applied Mathematical Modelling, 40(3), pp. 2134-2142. ISSN (print) 0307-904X

Jones, Mark (2015) Group equivariant singularity theory in the bifurcation of interfacial Wilton ripples. International Journal of Bifurcation and Chaos, 25(11), e1550147. ISSN (print) 0218-1274

Jones, M. (2011) The bifurcation of interfacial capillary-gravity waves under O(2) symmetry. Communications on Pure and Applied Analysis, 10(4), pp. 1183-1204.

Jones, M.C.W. (2010) On 1:2 resonant waves which arise between two stratified fluids of finite vertical extent in the presence of mean flow effects. European Journal of Mechanics B/Fluids, 29(5), pp. 395-402. ISSN (print) 0997-7546

Jones, M.C.W. (2007) Internal waves caused by the interaction of three harmonics under no restoring forces. Applied Mathematics Letters, 20(7), pp. 723-728. ISSN (print) 0893-9659

Jones, Mark (2001) On the evolution and stability of interfacial ripples on and off the critical frequency. Geophysical and Astrophysical Fluid Dynamics, 93(3/4), pp. 143-172. ISSN (print) 0309-1929

Jones, Mark (2001) On nonlinearly detuned third harmonic ripples between two stratified fluids. Quarterly of Applied Mathematics, 59(2), pp. 241-268. ISSN (print) 0033-569X

Jones, Mark (2000) A codimension seven unfolding of a third harmonic resonant interaction between two contiguous continua. Zeitschrift fuer Angewandte Mathematik und Physik, 51(5), pp. 651-673. ISSN (print) 0044-2275

Jones, M. (1999) A nonlinear multiple scales approach to modelling almost third harmonic interfaces. Zeitschrift für Angewandte Mathematik und Physik, 50(1), pp. 47-63. ISSN (print) 0044-2275

Jones, M. (1999) Nonlinear nearly Wilton ripples between two uniform stream flows. The Quarterly Journal of Mechanics and Applied Mathematics, 52(2), pp. 237-252. ISSN (print) 1464-3855

Jones, M. (1997) A new system of equations which predicts the evolution of a wave packet due to a fluid-fluid interaction under a narrow bandwidth assumption. Fluid Dynamics Research, 21(6), pp. 455-475. ISSN (print) 0169-5983

Jones, M. (1997) Group invariances, unfoldings and the bifurcation of capillary-gravity waves. International Journal of Bifurcation and Chaos (ijbc), 7(6), pp. 1243-1266. ISSN (print) 0218-1274

Jones, M.C.W. (1997) Nonlinear ripples of Kelvin-Helmholtz type which arise from an interfacial mode interaction. Journal of Fluid Mechanics, 341, pp. 295-315. ISSN (print) 0022-1120

Jones, M. (1996) Group invariances and second and third harmonic resonant capillary-gravity waves. Computers & Mathematics with Applications, 32(10), pp. 59-90. ISSN (print) 0898-1221

Jones, Mark (1996) Evolution equations and stability results for finite-depth Wilton ripples. International Journal of Non-Linear Mechanics, 31(1), pp. 41-58. ISSN (print) 0020-7462

Jones, M. (1995) On the stability of a wavetrain caused by interacting wave modes. Rocky Mountain Journal of Mathematics, 25(1), pp. 299-313. ISSN (print) 0035-7596

Jones, M.C.W. (1995) Evolution equations which model the ripples arising from an adjacent mode interaction. Dynamics and Stability of Systems, 10, pp. 163-178. ISSN (print) 1468-9367

Jones, M.C.W. (1994) Further results on the stability of symmetric and asymmetric resonant capillary-gravity waves. Japan Journal of Industrial and Applied Mathematics, 11(3), pp. 465-483. ISSN (print) 0916-7005

Jones, M. (1994) On the stability of finite-depth capillary-gravity waves by means of the fourth order evolution equation. Canadian Applied Mathematics Quarterly, 2(3), pp. 325-348. ISSN (print) 1073-1849

Jones, M.C.W. (1993) On coupled differential equations which model the evolution of interacting capillary-gravity wave modes and related questions of stability. IMA Journal of Applied Mathematics, 50(1), pp. 13-28. ISSN (print) 0272-4960

Jones, M. (1992) Nonlinear stability of resonant capillary-gravity waves. Wave Motion, 15(3), pp. 267-283. ISSN (print) 0165-2125

Jones, M. C. W. (1992) On the stability of a third harmonic resonant wavetrain. Stability and Applied Analysis of Continuous Media, 2, pp. 323-338. ISSN (print) 1120-4222

Jones, M. (1991) A non-uniqueness theorem in the theory of Voronoi sets. International Journal of Mathematics and Mathematical Sciences, 14(4), pp. 817-820. ISSN (print) 0161-1712

Jones, M. Christopher W. (1990) A public key cryptosystem as hard as a factorisation. Irish Mathematical Society Bulletin, 24, pp. 59-66. ISSN (print) 0790-1690

This list was generated on Sun Jun 16 07:21:38 2024 BST.