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- W2952714078 abstract "According to its Lax pair formulation, the nonlinear Schrodinger (NLS) equation can be expressed as the compatibility condition of two linear ordinary differential equations with an analytic dependence on a complex parameter. The first of these equations---often referred to as the emph{$x$-part} of the Lax pair---can be rewritten as an eigenvalue problem for a Zakharov-Shabat operator. The spectral analysis of this operator is crucial for the solution of the initial value problem for the NLS equation via inverse scattering techniques. For space-periodic solutions, this leads to the existence of a Birkhoff normal form, which beautifully exhibits the structure of NLS as an infinite-dimensional completely integrable system. In this paper, we take the crucial steps towards developing an analogous picture for time-periodic solutions by performing a spectral analysis of the emph{$t$-part} of the Lax pair with a periodic potential." @default.
- W2952714078 created "2019-06-27" @default.
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- W2952714078 date "2018-07-19" @default.
- W2952714078 modified "2023-10-01" @default.
- W2952714078 title "On the spectral problem associated with the time-periodic nonlinear Schrodinger equation" @default.
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