Solitons of the constrained Schrödinger equations

Abstract We consider the linear vector Schrödinger equation subjected to quadratic constraints. We demonstrate that the resulting nonlinear system is closely related to the Ablowitz-Ladik hierarchy and use this fact to derive the N -soliton solutions for the discussed model. As an example of application of these results we present solitons of some vector nonlinear Schrödinger equation with gradient nonlinearity.