Abstract
It is shown that a large subset of initial data with finite energy (L 2 norm) evolves nearly linearly in nonlinear Schrödinger equation with periodic boundary conditions. These new solutions are not perturbations of the known ones such as solitons, semiclassical or weakly linear solutions.
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Communicated by P. Constantin
The authors were partially supported by NSF grants DMS-0505216 (V. Z.) and DMS-0600101 (B. E.).
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Erdoğan, M.B., Zharnitsky, V. Quasi-Linear Dynamics in Nonlinear Schrödinger Equation with Periodic Boundary Conditions. Commun. Math. Phys. 281, 655–673 (2008). https://doi.org/10.1007/s00220-008-0454-0
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DOI: https://doi.org/10.1007/s00220-008-0454-0