Kevrekidis s interests are centered around the nonlinear dynamics of solitary waves in nonlinear partial differential equations and in lattice nonlinear differential difference equations and the properties ( existence, stability, dynamics ) of such waves.
32.
In spite of his observations of solitons in wave tank experiments, Scott Russell never recognized them as such, because of his focus on the " great wave of translation, " the largest amplitude solitary wave.
33.
If the spectrum of the operator is reduced to one single eigenvalue, its corresponding motion is that of a single bump that propagates at constant velocity and without deformation, a solitary wave called a " soliton ".
34.
During the highest tides on the upper reaches of this stretch, the rising water is funnelled up the estuary into the Severn bore, a self-reinforcing solitary wave that travels rapidly upstream against the river current.
35.
Solitary wave phenomena had been a 19th-century mystery dating back to work by John Scott Russell who, in 1834, observed what we now call a soliton, propagating in a canal, and chased it on horseback.
36.
Initially he thought that the stern could be a mirror of the stem, but soon realised that the removing water produced something closer to conventional waves than his solitary waves and ended up with a rounded stern with a catenary shape.
37.
The Severn bore is not a self-reinforcing solitary wave or soliton but rather a shock wave which is formed because the wave is travelling faster than the wave speed in water above the bore ( see tidal bore for more details ).
38.
So solitary waves on a water surface are " near "-solitons, but not exactly after the interaction of two ( colliding or overtaking ) solitary waves, they have changed a bit in amplitude and an oscillatory residual is left behind.
39.
So solitary waves on a water surface are " near "-solitons, but not exactly after the interaction of two ( colliding or overtaking ) solitary waves, they have changed a bit in amplitude and an oscillatory residual is left behind.
40.
The relationship between solitons & mdash; a self-reinforcing solitary wave ( a wave packet or pulse ) that maintains its shape while it travels at constant speed & mdash; and the low-frequency phonons in proteins have been discussed in a recent paper.
