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 ${\mathbb{R}}^N$, which involves equations with critical power nonlinearities and Hardy-type singular potentials. The equations are coupled by what we call ``Schrödinger-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 $\nu$. Moreover, by using min-max arguments, we seek bound states under some energy assumptions.

26 pages, 3 figures. arXiv admin note: text overlap with arXiv:2107.03737