MARK ALBER
Department of Mathematics
University of Notre Dame
Notre Dame, IN 46556-5683, USA
mark.s.alber.1@nd.edu
Abstract:
Piecewise modeling is widely used in the theory of nonlinear dynamical
systems with applications in engineering and biology. Recently peakon type
(piecewise wave) solutions of the evolution
equations became the subject of an active research effort.
In this talk we demonstrate some special features of the integrable evolution equations admitting piecewise solutions that differentiate these equations from those whose solutions are smooth, such as the KdV equation.
Then we describe a method of constructing weak piecewise wave solutions of such equations consisting of different pieces of profiles glued together at the peak points and describe propagation of the peaks in the context of the level set theory.