Bound and ground states of coupled NLS-KDV equations with Hardy potential and critical power

We consider the existence of bound and ground states for a family of nonlinear elliptic systems in $mathbb{R}^N$, which involves equations with critical power nonlinearities and Hardy-type singular potentials. The equations are coupled by what we call ``Schrodinger-Korteweg-de Vries non-symmetric terms, which arise in some phenomena of fluid mechanics. By means of variational methods, ground states are derived for several ranges of the positive coupling parameter $ u$. Moreover, by using min-max arguments, we seek bound states under some energy assumptions.