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- W2469852054 abstract "We prove symplectic non-squeezing (in the sense of Gromov) for the cubic nonlinear Schrodinger equation on $R^2$. This is the first symplectic non-squeezing result for a Hamiltonian PDE in infinite volume. As the underlying symplectic Hilbert space is $L^2(R^2)$, this requires working with initial data in this space. This space also happens to be scaling-critical for this equation. Thus, we also obtain the first unconditional symplectic non-squeezing result in such a critical setting. More generally, we show that solutions of this PDE can be approximated by a finite-dimensional Hamiltonian system, despite the wealth of non-compact symmetries: scaling, translation, and Galilei boosts. This approximation result holds uniformly on bounded sets of initial data. Complementing this approximation result, we show that all solutions of the finite-dimensional Hamiltonian system can be approximated by the full PDE. A key ingredient in these proofs is the development of a general methodology for obtaining uniform global space-time bounds for suitable Fourier truncations of dispersive PDE models." @default.
- W2469852054 created "2016-07-22" @default.
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- W2469852054 date "2016-06-24" @default.
- W2469852054 modified "2023-10-18" @default.
- W2469852054 title "Finite-dimensional approximation and non-squeezing for the cubic nonlinear Schrodinger equation on $R^2$" @default.
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- W2469852054 doi "https://doi.org/10.48550/arxiv.1606.07738" @default.
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