Mark David Groves is at present Professor at Saarland University in Saarbrücken, Germany. He will be Visiting Professor at the Centre for Mathematical Sciences, Lund University.

Even though water waves are some of the most common examples of wave motion, their mathematical interpretation is surprisingly difficult. The problem stems from the high degree of non-linearity of equations, which describe water waves. Therefore, researchers have been able to describe only certain aspects of such a motion in their simplified models.

The proposed project will develop a more complete model with focus on deeper understanding of solitary waves. Solitary waves can travel long distances with a constant shape and velocity. A British engineer, John Scott Russell, discovered such a wave first in 1834. He followed it for several kilometers along the Union canal between Glasgow and Edinburgh. Mathematical descriptions of such waves have found many applications, for example, in fiber optics and information technology.

While the wave observed by Russell was two-dimensional, since it exhibited no movement in the direction perpendicular to the direction of its progress, a theory of three-dimensional solitary waves has been initiated over the last ten years.

However, so far the progress of the theory has been limited by the physically unreasonable assumption of strong surface tension relative to the water’s depth. The project will study three-dimensional solitary waves in the presence of weak surface tension. The participation of Mark Groves, a world expert on non-linear mathematics of water waves, may make it possible to reach higher level of understanding of three-dimensional water waves.

Photo Loughborough University