We study the ground-state properties of a one-dimensional Bose gas with
N-body attractive contact interactions. By using the explicit form of the bright soliton solution of a generalized nonlinear Schr\"odinger equation, we compute the chemical potential and the ground-state energy. For
N=3, a localized soliton wave function exists only for a critical value of the interaction strength: in this case the ground state has an infinite degeneracy that can be parametrized by the chemical potential. The stabilization of the bright soliton solution by an external harmonic trap is also discussed, and a comparison with the effect of
N-body attractive contact interactions in higher dimensions is presented.
Using unitary and similarity transformations, explicit solutions of the coupled Gross–Pitaevskii models with spin–orbit coupling and varying nonlinearities and harmonic plus linear potentials are constructed by a mapping to the integrable one-dimensional Manakov system under the constraints of weak Raman coupling and small amplitude waves. An intriguing example for controllability of the dynamics is obtained for the case of a linear potential that induces complex spatial curvatures onto the density profiles. Perigrine solitons are also found demonstrating that the system may sustain rogue waves. It is shown that adiabatic modulations of external potentials and/or two-body atomic interactions may be used to efficiently control the dynamics of the constructed nonlinear waves. Numerical simulations demonstrate the stability of the obtained solutions.