Erwin Suazo (University of Puerto Rico at Mayaguez &Arizona State University): Transformations on the Study of Evolution Equations

This presentation is a continuation of my last
presentation in March.
This time we will show how some of the results of my last presentation
allow us to deduce transformations reducing the study of nonautonomous
(with time-dependent coefficients) and inhomogeneous (with space-dependent
coefficients) nonlinear Schroedinger equations (NLS) to the standard
autonomous nonlinear Schroedinger equation. The latter is a well-known
complete integrable system with Lax-Zakharov-Shabat pair, explaining the
integrability properties found in the past years for several researchers
in nonautonomous and inhomogeneous generalizations of NLS. Similarly we
will study these types of transformations for the analogous diffusion-type
equation that includes as particular cases the heat, cable, Fokker-Planck
and Black-Scholes equation and relates to Burgers-type equation and its
traveling wave solutions. Similar results have been found by Konotop et.
al. back in 2006. Most of the work presented here is the result of joint
work with Sergei K. Suslov.

Keywords: Lens transform, Cole-Hopf transformation, NLS, diffusion-type
equation.