Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2008-03-12
Nonlinear Sciences
Exactly Solvable and Integrable Systems
Scientific paper
In this paper we show that non-smooth functions which are distributional traveling wave solutions to the two component Camassa-Holm equation are distributional traveling wave solutions to the Camassa-Holm equation provided that the set $u^{-1}(c)$, where $c$ is the speed of the wave, is of measure zero. In particular there are no new peakon or cuspon solutions beyond those already satisfying the Camassa-Holm equation. However, the two component Camassa-Holm equation has distinct from Camassa-Holm equation smooth traveling wave solutions as well as new distributional solutions when the measure of $u^{-1}(c)$ is not zero. We provide examples of such solutions.
No associations
LandOfFree
A note on traveling wave solutions to the two component Camassa-Holm equation 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 A note on traveling wave solutions to the two component Camassa-Holm equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A note on traveling wave solutions to the two component Camassa-Holm equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-69293