Abstract
Our aim is to study the large time asymptotics of solutions to the fourth-order nonlinear Schrödinger equation in two space dimensions [Formula: see text] where [Formula: see text] We show that the nonlinearity has a dissipative character, so the solutions obtain more rapid time decay rate comparing with the corresponding linear case, if we assume the nonzero total mass condition [Formula: see text] We continue to develop the factorization techniques. The crucial points of our approach presented here are the [Formula: see text] — estimates of the pseudodifferential operators and the application of the Kato–Ponce commutator estimates.
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