Bound and ground states of coupled “NLS-KdV” equations with Hardy potential and critical power

Abstract. We consider the existence of bound and ground states for a family of nonlinear elliptic systems in R , which involves equations with critical power nonlinearities and Hardytype singular potentials. The equations are coupled by what we call “Schrödinger-Kortewegde 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 ν. Moreover, by using min-max arguments, we seek bound states under some energy assumptions.

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