  This paper focuses on traveling wave solutions for the so-called
Rosenzweig-MacArthur model with spatial diffusion. The main results of this
note are concerned with the existence and uniqueness of traveling wave solution
as well as periodic wave train solution in the large wave speed asymptotic.
Depending on the model parameters we more particularly study the existence and
this uniqueness of a traveling wave connecting two equilibria or connecting an
equilibrium point and a periodic wave train. We also discuss the existence and
uniqueness of such a periodic wave train. Our analysis is based on ordinary
differential techniques by coupling the theories of invariant manifolds
together with those of global attractors.
