The Zero-Dispersion Limit for the Odd Flows in the Focusing Zakharov-Shabat Hierarchy

Details The Zero-Dispersion Limit for the Odd Flows in the Focusing Zakharov-Shabat Hierarchy The Zero-Dispersion Limit for the Odd Flows in the Focusing Zakharov-Shabat Hierarchy

2003-02-03

arxiv.org/abs/nlin/0302003v1

IMRN 2003, no. 47, 2529-2564

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

We present a numerical and theoretical study of the zero-dispersion limit of the focusing Zakharov-Shabat hierarchy, which includes NLS and mKdV flows as its second and third members. All the odd flows in the hierachy are shown to preserve real-valued data. We establish the zero-dispersion limit of all the nontrivial conserved densities and associated fluxes for these odd flows for a large class of real-valued initial data which includes all ``single hump'' initial data. In particular, it is done for the ``focusing'' mKdV flow. The method is based on the Lax-Levermore KdV strategy, but here it is carried out in the context of a nonselfadjoint spectral problem. We find that after an algebraic transformation the limiting dynamics of the mKdV equation is identical to that of the KdV equation.

Affiliated with

Also associated with

No associations

Rating

The Zero-Dispersion Limit for the Odd Flows in the Focusing Zakharov-Shabat Hierarchy 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 The Zero-Dispersion Limit for the Odd Flows in the Focusing Zakharov-Shabat Hierarchy, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Zero-Dispersion Limit for the Odd Flows in the Focusing Zakharov-Shabat Hierarchy will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-350398