Bifurcation diagram of a one-parameter family of dispersive waves

Details Bifurcation diagram of a one-parameter family of dispersive waves Bifurcation diagram of a one-parameter family of dispersive waves

1997-07-24

arxiv.org/abs/solv-int/9707011v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

latex2e, 28 pages, 14 figures, revised version to appear in Matematica Contemporanea 2000. Substantial changes and improvement

Scientific paper

The Korteweg de Vries (KdV) equation with small dispersion is a model for the formation and propagation of dispersive shock waves in one dimension. Dispersive shock waves in KdV are characterized by the appearance of zones of rapid modulated oscillations in the solution of the Cauchy problem with smooth initial data. The modulation in time and space of the amplitudes, the frequencies and the wave-numbers of these oscillations and their interactions is approximately described by the $g$-phase Whitham equations. We study the initial value problem for the Whitham equations for a one parameter family of monotone decreasing initial data. We obtain the bifurcation diagram of the number $g$ of interacting oscillatory zones.

Affiliated with

Also associated with

No associations

Rating

Bifurcation diagram of a one-parameter family of dispersive 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 Bifurcation diagram of a one-parameter family of dispersive waves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bifurcation diagram of a one-parameter family of dispersive waves will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-662209