Nontrivial class of composite $U(\sigma+\mu)$ vector solitons

A mixed problem for the compact $U(m)$ vector nonlinear Schrödinger model with an arbitrary sign of coupling constant is exactly solved. It is shown that a new class of solutions—composite $U(\sigma+\mu)$ vector solitons with inelastic interaction (changing shape without energy loss) at $\sigma>1$ and strictly elastic interaction at $\sigma=1$— exists for $m\geq3$. These solitons are color structures consisting of $\sigma$ bright and $\mu$ dark solitons ($\sigma+\mu=m$) and capable of existing in both self-focusing and defocusing media. The $N$-soliton formula universal for attraction and repulsion is derived by the Hirota method.