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Failure of scattering to solitary waves for long-range nonlinear Schrödinger equations
Discrete and Continuous Dynamical Systems ( IF 1.1 ) Pub Date : 2020-09-15 , DOI: 10.3934/dcds.2020328
Jason Murphy , , Kenji Nakanishi ,

We consider nonlinear Schrödinger equations with either power-type or Hartree nonlinearity in the presence of an external potential. We show that for long-range nonlinearities, solutions cannot exhibit scattering to solitary waves or more general localized waves. This extends the well-known results concerning non-existence of non-trivial scattering states for long-range nonlinearities.

中文翻译:

远程非线性Schrödinger方程的孤立波散射失败

在存在外部电势的情况下,我们考虑具有功率类型或Hartree非线性的非线性Schrödinger方程。我们表明,对于远距离非线性,解决方案不能表现出对孤立波或更普遍的局部波的散射。这扩展了关于不存在用于长距离非线性的非平凡散射状态的众所周知的结果。
更新日期:2020-09-15
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