Abstract:
We study the large-time behaviour of solutions
of the Cauchy problem for a non-linear
Schrödinger equation. We consider the interaction
between the resonance term and other
types of non-linearity.
We prove that solutions exist globally
in time and find a large-time asymptotic
representation for them.
We show that the decay of solutions in the
far region has the same order as in the linear
case, while the solutions in the short-range
region acquire an additional logarithmic decay,
which is slower than in the case when there
is no resonance term in the original
equation.
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