  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 Schroedinger 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 parameterized 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.
