## Generalized solutions to GKDV equation

Autores:
M. M. Melo
Resumo:
In this article we study the Cauchy problem in $\mathcal{G}_2((0,T)×\times \mathbf{R})$ (the algebra of the generalized functions, in the sense of Colombeau) for the generalized Korteweg-de Vries equation, with initial data $\varphi \in \mathcal{G}_2(\mathbf{R})$, which contains $H^s(\mathbf{R})$ for all $s \in \mathbf{R}$.