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On Schrödinger systems with cubic dissipative nonlinearities of derivative type (1507.07617v1)
Published 28 Jul 2015 in math.AP
Abstract: Consider the initial value problem for systems of cubic derivative nonlinear Schr\"odinger equations in one space dimension with the masses satisfying a suitable resonance relation. We give structural conditions on the nonlinearity under which the small data solution gains an additional logarithmic decay as $t \to +\infty$ compared with the corresponding free evolution.