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

[摘要] We consider the final-state problem for the nonlinear Schrodinger equations (NLS) with a suitable time-decaying harmonic oscillator. In this equation, the power of nonlinearity vertical bar u vertical bar(rho)u is included in the long-range class if 0 < rho <= 2/(n(1 - lambda)) with 0 <= 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. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-01

[关键词] Nonlinear scattering theory;Long-range scattering;Time-dependent harmonic oscillators;Final state problem