Mark Groves

Professor of Mathematics
Department of Mathematical Sciences
Loughborough University
Loughborough
Leicestershire
LE11 3TU
UK

Email: M.D.Groves@lboro.ac.uk

Contact me at Universität des Saarlandes, Saarbrücken, Germany:

Tel: +49 681 302 57421
Email: groves@math.uni-sb.de
My homepage in Saarbrücken

Research activities

• Nonlinear partial differential equations
• Hamiltonian systems
• Water waves
• Spatial dynamics
• Calculus of variations

The talk I gave for my habilitation at Stuttgart (Periodische Lösungen nichtlinearer Wellengleichungen)

My plenary talk at the 2003 Equadiff conference in Hasselt, Belgium and the 2006 GAMM annual meeting in Berlin (Nonlinear water waves and spatial dynamics).

Some further talks:

• A dimension-breaking phenomenon in the theory of steady gravity-capillary water waves
• Modulating pulse solutions for a class of nonlinear wave equations
• Nichtlineare Wasserwellen und räumliche Dynamik
• Three-dimensional solitary gravity-capillary water waves
• Moving breather solutions to a class of quasilinear Klein-Gordon equations
• Existence and stability of fully localised three-dimensional gravity-capillary water waves

This doubly periodic water wave was disussed by M. D. Groves & M. Haragus in "A bifurcation theory for three-dimensional oblique travelling gravity-capillary water waves", J. Nonlinear Sci. 13, 397-447 (2003).

These oblique solitary water waves were disussed by M. D. Groves & M. Haragus in "A bifurcation theory for three-dimensional oblique travelling gravity-capillary water waves", J. Nonlinear Sci. 13, 397-447 (2003).

This oblique generalised solitary water wave was disussed by M. D. Groves & M. Haragus in "A bifurcation theory for three-dimensional oblique travelling gravity-capillary water waves", J. Nonlinear Sci. 13, 397-447 (2003).

This dimension breaking phenomenon was disussed by M. D. Groves, M. Haragus & S. M. Sun in "A dimension-breaking phenomenon in the theory of gravity-capillary water waves", Phil. Trans. Roy. Soc. A 360, 2337-2358 (2002).

This water wave is periodic in the direction of propagation and has a solitary-wave profile in the transverse direction. It, and its multipulse generalisations, were discussed by M. D. Groves & B. Sandstede in "A plethora of three-dimensional periodic travelling gravity-capillary water waves with multipulse transverse profiles", J. Nonlinear Sci. 14, 297-340 (2004).

These waves were found using the "spatial dynamics" method. An informal introduction to this method and a catalogue of further water waves which can be found using it is available here (and in German here.)

This fully localised solitary water wave is the subject of a submitted paper by M. D. Groves & S. M. Sun.

• Tsunamis
• Solitons
• The KP page
• Mark Cramer's gallery of fluid mechanics
• Rogue waves by Günther Clauss

Journal publications since 2001

• A spatial dynamics approach to three-dimensional steady gravity-capillary water waves
  M. D. Groves and A. Mielke, Proc. Roy. Soc. Edinburgh A 31, 83-136 (2001)
• An existence theory for three-dimensional periodic travelling gravity-capillary water waves with bounded transverse profiles
  M. D. Groves Physica D 31, 152-153, 395-415 (2001)
• Modulating pulse solutions for a class of nonlinear wave equations
  M. D. Groves and G. Schneider, Comm. Math. Phys. 219, 489-522 (2001).
• Transverse instability of line gravity-capillary solitary water waves
  M. D. Groves, M. Haragus and S. M. Sun, C. R. Acad. Sci. Paris 333, 421-426 (2001).
• A dimension-breaking phenomenon in the theory of gravity-capillary water waves
  M. D. Groves, M. Haragus and S. M. Sun, Phil. Trans. Roy. Soc. Lond. A 360, 2337-2358 (2002).
• A bifurcation theory for three-dimensional oblique travelling gravity-capillary water waves
  M. D. Groves and M. Haragus, J. Nonlinear Sci. 13, 397-447 (2003).
• A plethora of three-dimensional periodic travelling gravity-capillary water waves with multipulse transverse profiles
  M. D. Groves and B Sandstede, J. Nonlinear Sci. 14, 297-340 (2004).
• Steady water waves
  M. D. Groves, J. Nonlinear Math. Phys. 11, 435-460 (2004).
• Modulating pulse solutions for quasilinear wave equations
  M. D. Groves and G. Schneider, J. Diff. Eqns. 219, 221-258 (2005).
• Three-dimensional travelling gravity-capillary water waves
  M. D. Groves, GAMM Mitteilungen. 30, 8-43 (2007).
• Spatial dynamics methods for solitary gravity-capillary water waves with an arbitrary distribution of vorticity
  M. D. Groves and E. Wahlén, SIAM J. Math. Anal. 39, 932-964 (2007).
• Fully localised solitary-wave solutions of the three-dimensional gravity-capillary water-wave problem
  M. D. Groves and S. M. Sun, Arch. Rat. Mech. Anal. 188, 1-91 (2008).
• Modulating pulse solutions to quadratic quasilinear wave equations over exponentially long length scales
  M. D. Groves and G. Schneider, Comm. Math. Phys. 278, 567-625 (2008).
• Small-amplitude Stokes and solitary gravity water waves with an arbitrary distribution of vorticity
  M. D. Groves and E. Wahlén, Physica D 237, 1530-1538 (2008).

The October 2002 issue of Phil. Trans. Roy. Soc. Lond. A is a theme issue entitled Recent developments in the mathematical theory of water waves, edited by W. Craig, M. D. Groves, G. Schneider and J. F. Toland.

The March 2007 issue of GAMM Mitteilungen is a theme issue entitled Nonlinear waves, edited by M. D. Groves.

Editorial work

I am an associate editor of the Wiley journal Mathematical Methods in the Applied Sciences