  In this paper we establish existence and stability results concerning fully
nontrivial solitary-wave solutions to 3-coupled nonlinear Schr\"odinger system
\[
  i\partial_t u_{j}+\partial_{xx}u_{j}+ \left(\sum_{k=1}^{3} a_{kj}
|u_k|^{p}\right)|u_j|^{p-2}u_j = 0, \ j=1,2,3, \] where $u_j$ are
complex-valued functions of $(x,t)\in \mathbb{R}^{2}$ and $a_{kj}$ are positive
constants satisfying $a_{kj}=a_{jk}$ (symmetric attractive case). Our approach
improves many of the previous known results. In all methods used previously to
study solitary waves, which we are aware of, the variational problem has
consisted of finding the extremum of an energy functional subject to the
constraints that were not independently chosen. Here we study a problem of
minimizing the energy functional subject to three independent $L^2$ mass
constraints and establish existence and stability results for a true
three-parameter family of solitary waves.
