We consider weakly interacting bosonic gases with local and nonlocal multibody interactions. By using the Bogoliubov approximation, we first investigate contact interactions, studying the case in which the interparticle potential can be written as a sum of N-body Î ́ interactions and then considering general contact potentials. Results for the quasiparticle spectrum and the stability are presented. We then examine nonlocal interactions, focusing on two different cases of three-body nonlocal interactions. Our results are used for systems with two- and three-body Î ́ interactions and applied for realistic values of the trap parameters. Finally, the effect of conservative three-body terms in dipolar systems and soft-core potentials (that can be simulated with Rydberg dressed atoms) is also studied.
