Abstract
The Generation, Propagation and Extinction of Multiphases
in the KdV Zero Dispersion Limit
Fei-Ran Tian
Ohio State University
We study the multiphases in the KdV zero dispersion limit. The phases are
governed by the Whitham equations which are $2g +1$ quasilinear hyperbolic
equations where $g$ is the number of phases. We are interested
in the interaction of two single phases for fairly general initial data.
We analyze in detail how a double phase is generated from the interaction,
how it propagates in space-time and how it collapses to a single phase
in a finite time.
The Whitham equations are known to be integrable via hodograph transform.
The crucial step in our approach is to formulate the hodograph transform
in terms of the Euler-Poisson-Darboux solution. Under our scheme, the zeros
of the Jacobian of the transform are determined by the zeros of the
Euler-Poisson-Darboux solution. Hence, the problem of inverting
hodograph transform to give the Whitham solution reduces to that of
counting the zeros of the Euler-Poisson-Darboux solution.
Return to
Return to conference page