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arXiv · 1909.11332

Failure of scattering to standing waves for a Schr\"{o}dinger equation with long-range nonlinearity on star graph

Kazuki Aoki·Takahisa Inui·Haruya Mizutani
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Abstract

We consider the Schr\"{o}dinger equation with power type long-range nonlinearity on star graph. Under a general boundary condition at the vertex, including Kirchhoff, Dirichlet, $\delta$, or $\delta'$ boundary condition, we show that the non-trivial global solution does not scatter to standing waves. Our proof is based on the argument by Murphy and Nakanishi, who treated the long-range nonlinear Schr\"{o}dinger equation with a general potential in the Euclidean space, in order to consider general boundary conditions.

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Kazuki Aoki, Takahisa Inui, Haruya Mizutani. 2019-09-25. Failure of scattering to standing waves for a Schr\"{o}dinger equation with long-range nonlinearity on star graph. https://arxiv.org/abs/1909.11332

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