We consider the (de)focusing cubic Gross-Pitaevskii (GP) hierarchy on $\mathbb{ R}$, which is an infinite hierarchy of coupled linear inhomogeneous PDE which appears in the derivation of the cubic nonlinear Schr\"{ o}dinger (NLS) equation from quantum many-particle systems. Motivated by the fact that the cubic NLS on $\mathbb{ R}$ is an integrable equation which admits infinitely many conserved quantities, we exhibit an infinite sequence of operators which generate analogous conserved quantities for the GP hierarchy.
Categories: math.AP math-ph math.MP