On long time behavior of the solutions of the coupled Zakharov-Kuznetsov system

Abstract

We consider the long time asymptotic behavior of the solutions of the coupled Zakharov-Kuznetsov system. Compared with the classical Zakharov-Kuznetsov equation, the linear coupling term coefficients and the convection term coefficients will not affect its well-posedness but will affect the local energy decay property. Two local energy decay results of the coupled Zakharov-Kuznetsov system are obtained when the initial data are in $L^2\left(R^2\right)\times L^2\left(R^2\right)$ and $H^1\left(R^2\right)\times H^1\left(R^2\right)$, respectively. The local decay results indicate the impossibility of the breather solutions for some coupled Zakharov-Kuznetsov system in a growing domain depending on time variable but not contains the soliton region.