Special solutions to a compact equation for deep-water gravity waves

Details Special solutions to a compact equation for deep-water gravity waves Special solutions to a compact equation for deep-water gravity waves

2012-04-13

arxiv.org/abs/1204.2889v1

Physics

Classical Physics

17 pages, 14 figures, 40 references. Other author's papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh/

Scientific paper

Recently, Dyachenko & Zakharov (2011) have derived a compact form of the well known Zakharov integro-differential equation for the third order Hamiltonian dynamics of a potential flow of an incompressible, infinitely deep fluid with a free surface. In this work, special traveling wave solutions of this compact equation are numerically constructed using the Petviashvili method. Their stability properties are also investigated. Further, unstable traveling waves with wedge-type singularities, viz. peakons, are numerically identified. An analytical solution of such peakons is derived also for a perturbed version of the compact equation. Finally, by means of an accurate Fourier-type spectral scheme it is found that smooth solitary waves appear to collide elastically, suggesting the integrability of the Zakharov equation.

Affiliated with

Also associated with

No associations

Rating

Special solutions to a compact equation for deep-water gravity waves 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 Special solutions to a compact equation for deep-water gravity waves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Special solutions to a compact equation for deep-water gravity waves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-143384