An infinite sequence of conserved quantities for the cubic Gross–Pitaevskii hierarchy on ℝ

Abstract

We consider the cubic Gross–Pitaevskii (GP) hierarchy on R \mathbb {R} , which is an infinite hierarchy of coupled linear inhomogeneous partial differential equations appearing in the derivation of the cubic nonlinear Schrödinger equation from quantum many-particle systems. In this work, we identify an infinite sequence of operators which generate infinitely many conserved quantities for solutions of the GP hierarchy.