Resolution of a shock in hyperbolic systems modified by weak dispersion

Details Resolution of a shock in hyperbolic systems modified by weak dispersion Resolution of a shock in hyperbolic systems modified by weak dispersion

2005-03-07

arxiv.org/abs/nlin/0503010v4

Chaos 15, 037103 (2005)

Nonlinear Sciences

Pattern Formation and Solitons

56 pages, 5 figures. Misprints corrected. References added

Scientific paper

10.1063/1.1947120

We present a way to deal with dispersion-dominated ``shock-type'' transition in the absence of completely integrable structure for the systems that one may characterize as strictly hyperbolic regularized by a small amount of dispersion. The analysis is performed by assuming that, the dispersive shock transition between two different constant states can be modelled by an expansion fan solution of the associated modulation (Whitham) system for the short-wavelength nonlinear oscillations in the transition region (the so-called Gurevich -- Pitaevskii problem). We consider as single-wave so bi-directional systems. The main mathematical assumption is that of hyperbolicity of the Whitham system for the solutions of our interest. By using general properties of the Whitham averaging for a certain class of nonlinear dispersive systems and specific features of the Cauchy data prescription on characteristics we derive a set of transition conditions for the dispersive shock, actually bypassing full integration of the modulation equations. Along with model KdV and mKdV examples, we consider a non-integrable system describing fully nonlinear ion-acoustic waves in collisionless plasma. In all cases our transition conditions are in complete agreement with previous analytical and numerical results.

Affiliated with

Also associated with

No associations

Rating

Resolution of a shock in hyperbolic systems modified by weak dispersion 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 Resolution of a shock in hyperbolic systems modified by weak dispersion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Resolution of a shock in hyperbolic systems modified by weak dispersion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-403713