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We consider the existence of bound and ground states for a family ofnonlinear elliptic systems in $\mathbb{R}^N$, which involves equations withcritical power nonlinearities and Hardy-type singular potentials. The equationsare coupled by what we call ``Schr\"odinger-Korteweg-de Vries'' non-symmetricterms, which arise in some phenomena of fluid mechanics. By means ofvariational methods, ground states are derived for several ranges of thepositive coupling parameter $\nu$. Moreover, by using min-max arguments, weseek bound states under some energy assumptions.

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