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arXiv · 2009.01526

Final state problem for nonlinear Schrödinger equations with time-decaying harmonic oscillators

Masaki Kawamoto
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Abstract

We consider the final-state problem for the nonlinear Schrödinger equations (NLS) with a suitable time-decaying harmonic oscillator. In this equation, the power of nonlinearity $|u|^ρu $ is included in the long-range class if $0 < ρ\leq 2/(n(1- λ)) $ with $0 \leq λ<1/2$, which is determined by the harmonic potential and a coefficient of Laplacian. In this paper, we find the final state for this system and obtain the decay estimate for asymptotics.

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Masaki Kawamoto. 2021-05-13. Final state problem for nonlinear Schrödinger equations with time-decaying harmonic oscillators. https://doi.org/10.1016/j.jmaa.2021.125292

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