Ground states of Bose–Einstein condensates with higher order interaction

Highlights: • Ground state exists for positive higher order interactions. • Ground state is unique with certain negative contact interaction. • Higher order interaction competes with contact interaction. • Thomas-Fermi limits are different in whole space and bounded domain. • Asymptotic profiles of ground states satisfy free boundary problems. -- Abstract: We analyze the ground state of a Bose–Einstein condensate in the presence of higher-order interaction (HOI), modeled by a modified Gross–Pitaevskii equation (MGPE). In fact, due to the appearance of HOI, the ground state structures become very rich and complicated. We establish the existence and non-existence results under different parameter regimes, and obtain their limiting behaviors and/or structures with different combinations of HOI and contact interactions. Both the whole space case and the bounded domain case are considered, where different structures of ground states are identified.