Invariant Borel probability measures for discrete long-wave-short-wave resonance equations

Abstract

In this article we study the Borel probability measures that can be associated to the time averaged observation of the process generated by the non-autonomous long-wave-short-wave resonance equations on infinite lattices, via the notion of generalized Banach limit. We establish that the generated process possesses a pullback-D attractor, and further prove that there exists a unique family of invariant Borel probability measures carried by the pullback attractor.