Discontinuous Ground States for NLSE on $\mathbb{R}$ with a F\"{u}l\"{o}p-Tsutsui $\delta$ interaction

Riccardo Adami; Takaaki Nakamura; Alice Ruighi

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arXiv · 2010.00895

Discontinuous Ground States for NLSE on $\mathbb{R}$ with a F\"{u}l\"{o}p-Tsutsui $\delta$ interaction

Riccardo Adami·Takaaki Nakamura·Alice Ruighi

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Abstract

We analyse the existence and the stability of the ground states of the one-dimensional nonlinear Schr\"{o}dinger equation with a focusing power nonlinearity and a defect located at the origin. In this paper a ground state is defined as a global minimizer of the action functional on the Nehari manifold and the defect considered is a F\"{u}l\"{o}p-Tsutsui $\delta$ type, namely a $\delta$ condition that allows discontinuities. The existence of ground states is proved by variational techniques, while the stability results from the Grillakis-Shatah-Strauss theory.

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Riccardo Adami, Takaaki Nakamura, Alice Ruighi. 2020-10-02. Discontinuous Ground States for NLSE on $\mathbb{R}$ with a F\"{u}l\"{o}p-Tsutsui $\delta$ interaction. https://arxiv.org/abs/2010.00895

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