CM2LA Seminar

Abstract:   It has been common practice for decades to approximate localized solutions of evolution equations set on unbounded spatial domains by solutions of associated periodic initial-value problems or Dirichlet problems.  We mention especially the work of Zabusky and Kruskal in the early 1960's, but we don't doubt that this practice goes back further, though not much further as computers of large enough scale to handle even one-space and one-time dimensional problems were not available much earlier.  Despite this method's long history, rigorous theory with error estimates is sparse.  

It is our purpose to sketch theory with error estimates for such methodology here.  This is done in the context of long-crested, surface water wave models.  The two models we analyze are both unidirectional, long-wave models.  While the theory is concretely attached to these models, one could formulate a more general theory if so desired.