Q-balls and charged Q-balls in a two-scalar field theory with generalized Henon-Heiles potential

We construct Q-ball solutions from a model consisting of one massive scalar field ξ and one massive complex scalar field φ interacting via the cubic couplings g₁ ξ φ* φ + g₂ ξ³, typical of Henon-Heiles-like potentials. Although being formally simple, these couplings allow for Q-balls. In one spatial dimension, analytical solutions exist, either with vanishing or non vanishing φ. In three spatial dimensions, we numerically build Q-ball solutions and investigate their behaviours when changing the relatives values of g₁ and g₂. For g₁<g₂, two Q-balls with the same frequency exist, while ω=0 can be reached when g₁>g₂. We then extend the former solutions by gauging the U(1)-symmetry of φ and show that charged Q-balls exist.