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

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 $|u{|}^{\rho }u$ is included in the long-range class if $0<\rho \le 2/(n(1-\lambda ))$ with $0\le \lambda <1/2$, 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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Cited by in corpus (2)

• Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials
• On Schrödinger equation with square and inverse-square potentials