On Schrödinger systems with cubic dissipative nonlinearities of derivative type

Abstract

Consider the initial value problem for systems of cubic derivative nonlinear Schrödinger 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.

26 pages

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