Quasi-linear dynamics in nonlinear Schr\" odinger equation with periodic boundary conditions
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🧮 math-ph
math.MP
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boundaryconditionsequationnonlinearodingerperiodicschrsolutions
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It is shown that a large subset of initial data with finite energy ($L^2$ norm)evolves nearly linearly in nonlinear Schr\" odinger 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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