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

Mendelson, Dana; Nahmod, Andrea; Pavlović, Nataša; Staffilani, Gigliola

doi:10.1090/tran/7726

An infinite sequence of conserved quantities for the cubic Gross–Pitaevskii hierarchy on $\mathbb {R}$
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by Dana Mendelson, Andrea R. Nahmod, Nataša Pavlović and Gigliola Staffilani PDF

Trans. Amer. Math. Soc. 371 (2019), 5179-5202 Request permission

Abstract:

We consider the cubic Gross–Pitaevskii (GP) hierarchy on $\mathbb {R}$, 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.

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