Exact solutions of the associated Camassa-Holm equation

Details Exact solutions of the associated Camassa-Holm equation Exact solutions of the associated Camassa-Holm equation

1999-01-24

arxiv.org/abs/solv-int/9901009v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages

Scientific paper

Recently the associated Camassa-Holm (ACH) equation, related to the Fuchssteiner-Fokas-Camassa-Holm equation by a hodograph transformation, was introduced by Schiff, who derived B\"{a}cklund transformations by a loop group technique and used these to obtain some simple soliton and rational solutions. We show how the ACH equation is related to Schr\"{o}dinger operators and the KdV hierarchy, and use this connection to obtain exact solutions (rational and N-soliton solutions). More generally, we show that solutions of ACH on a constant background can be obtained directly from the tau-functions of known solutions of the KdV hierarchy on a zero background. We also present exact solutions given by a particular case of the third Painlev\'{e} transcendent.

Affiliated with

Also associated with

No associations

Rating

Exact solutions of the associated 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 Exact solutions of the associated Camassa-Holm equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exact solutions of the associated Camassa-Holm equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-637542