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arXiv · 1612.09236

An infinite sequence of conserved quantities for the cubic Gross-Pitaevskii hierarchy on $\mathbb{R}$

Dana Mendelson·Andrea Nahmod·Nataša Pavlović·Gigliola Staffilani
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Abstract

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.

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Dana Mendelson, Andrea Nahmod, Nataša Pavlović, Gigliola Staffilani. 2016-12-29. An infinite sequence of conserved quantities for the cubic Gross-Pitaevskii hierarchy on $\mathbb{R}$. https://arxiv.org/abs/1612.09236

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