Long-Time Dynamics of KdV Solitary Waves over a Variable Bottom

Details Long-Time Dynamics of KdV Solitary Waves over a Variable Bottom Long-Time Dynamics of KdV Solitary Waves over a Variable Bottom

2004-11-17

arxiv.org/abs/math-ph/0411059v1

Physics

Mathematical Physics

33 pages

Scientific paper

We study the variable bottom generalized Korteweg-de Vries (bKdV) equation dt u=-dx(dx^2 u+f(u)-b(t,x)u), where f is a nonlinearity and b is a small, bounded and slowly varying function related to the varying depth of a channel of water. Many variable coefficient KdV-type equations, including the variable coefficient, variable bottom KdV equation, can be rescaled into the bKdV. We study the long time behaviour of solutions with initial conditions close to a stable, b=0 solitary wave. We prove that for long time intervals, such solutions have the form of the solitary wave, whose centre and scale evolve according to a certain dynamical law involving the function b(t,x), plus an H^1-small fluctuation.

Affiliated with

Also associated with

No associations

Rating

Long-Time Dynamics of KdV Solitary Waves over a Variable Bottom does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Long-Time Dynamics of KdV Solitary Waves over a Variable Bottom, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Long-Time Dynamics of KdV Solitary Waves over a Variable Bottom will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-258394