Nonlinear Schrödinger equations with exceptional potentials

Ivan Naumkin

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arXiv · 1707.00503

Nonlinear Schrödinger equations with exceptional potentials

Ivan Naumkin

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Abstract

We consider the cubic nonlinear Schrödinger equation with an exceptional potential. We obtain a sharp time decay for the global in time solution and we get the large time asymptotic profile of small solutions. We prove the existence of modified scattering for this model, that is, linear scattering modulated by a phase. Our approach is based on the spectral theorem for the perturbed linear Schrödinger operator and a factorization technique, that allows us to control the resonant nonlinear term. We make some parity assumptions in order to control the small-energy behavior of the scattering coefficients and of the wave functions.

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Ivan Naumkin. 2017-07-08. Nonlinear Schrödinger equations with exceptional potentials. https://arxiv.org/abs/1707.00503

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