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• W2980488876 abstract "We consider the cubic Gross-Pitaevskii (GP) hierarchy in one spatial dimension. We establish the existence of an infinite sequence of observables such that the corresponding trace functionals, which we call ``energies,'' commute with respect to the weak Lie-Poisson structure defined by the authors in arXiv:1908.03847. The Hamiltonian equation associated to the third energy functional is precisely the GP hierarchy. The equations of motion corresponding to the remaining energies generalize the well-known nonlinear Schrodinger hierarchy, the third element of which is the one-dimensional cubic nonlinear Schrodinger equation. This work provides substantial evidence for the GP hierarchy as a new integrable system." @default.
• W2980488876 created "2019-10-25" @default.
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• W2980488876 date "2019-10-15" @default.
• W2980488876 modified "2023-09-27" @default.
• W2980488876 title "Poisson Commuting Energies for a System of Infinitely Many Bosons" @default.
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• W2980488876 hasPublicationYear "2019" @default.
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