Abstract
The Cauchy problem for the Schrödinger equation with a monomial nonlinear term is considered. Under a growth condition on the nonlinear term, it is shown that low energy, exponentially decaying initial data yield a global solution which is analytic in its space variables and whose domain of analyticity expands in time. It is also shown that low energy analytic initial data on a symmetric tube domain lead to a global solution which is analytic on the same tube domain for all time.
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Communicated by P. Constantin
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Nakamitsu, K. Analytic Finite Energy Solutions of the Nonlinear Schrödinger Equation. Commun. Math. Phys. 260, 117–130 (2005). https://doi.org/10.1007/s00220-005-1405-7
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DOI: https://doi.org/10.1007/s00220-005-1405-7