Fifth order KdV-BBM model for unidirectional water waves

In this talk we introduce a  fifth order  mathematical model  that describes water waves propagating mainly in one direction. This model is analogous to the first-order approximations of the KdV- or BBM-type. We discuss the  local well-posedness theory for the associated initial value problem  (IVP) using a contraction mapping argument. A subclass of this model possesses a special Hamiltonian structure that implies the local theory can be continued indefinitely. We also prove that the local solution to the associated IVP  for given data in the spaces of functions analytic on a strip around the real axis continues to be analytic without shrinking the width of the strip in time. Finally, we study the evolution in time of the radius of spatial analyticity and show that it decreases as the time advances. Finally, we present a lower bound on the possible rate of decrease in time of the uniform radius of spatial analyticity.