Solutions of the Korteweg - de Vries equation in spaces containing unbounded functions
John Gonzalez

Abstract: The KdV equation was discovered by Boussinesq at the end of 19th century but went unnoticed until papers by Korteweg and de Vries who investigated behavior of solitary waves (or solitons) that were observed experimentally by Scott Russell in shallow water. Later the equation appeared in various parts of mathematics, electronics, plasma physics, and biology among other areas. It is a universal equation for 1D nonlinear dispersive waves and solutions have been constructed by various methods including the inverse scattering method. In the early 1980's Bondareva and Shubin proved existence and uniqueness of solutions when the initial data lies in certain spaces containing unbounded functions. I will describe some of these results and the methods used.