# American Institute of Mathematical Sciences

doi: 10.3934/dcdsb.2021311
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## Statistical solution and Liouville type theorem for coupled Schrödinger-Boussinesq equations on infinite lattices

 1 Department of Data science and Big data technology, Wenzhou University, Wenzhou, Zhejiang 325035, China 2 Department of Mathematics, Wenzhou University, Wenzhou, Zhejiang 325035, China

* Corresponding author: Chunqiu Li

Received  August 2021 Revised  November 2021 Early access January 2022

In this article, we are concerned with statistical solutions for the nonautonomous coupled Schrödinger-Boussinesq equations on infinite lattices. Firstly, we verify the existence of a pullback-${\mathcal{D}}$ attractor and establish the existence of a unique family of invariant Borel probability measures carried by the pullback-${\mathcal{D}}$ attractor for this lattice system. Then, it will be shown that the family of invariant Borel probability measures is a statistical solution and satisfies a Liouville type theorem. Finally, we illustrate that the invariant property of the statistical solution is indeed a particular case of the Liouville type theorem.

Citation: Congcong Li, Chunqiu Li, Jintao Wang. Statistical solution and Liouville type theorem for coupled Schrödinger-Boussinesq equations on infinite lattices. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021311
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