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arXiv · 2305.19791

On the focusing fractional nonlinear Schr\"{o}dinger equation on the waveguide manifolds

Amin Esfahani·Hichem Hajaiej·Yongming Luo·Linjie Song
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Abstract

In this paper, we consider the focusing fractional nonlinear Schr\"{o}dinger equation (FNLS) on the waveguide manifolds $\mathbb{R}^d\times\mathbb{T}^m$ both in the isotropic and anisotropic case. Under different conditions, we establish the existence and periodic dependence of the ground states of the focusing FNLS. In the intercritical regime, we also establish the large data scattering for the anisotropic focusing FNLS by appealing to the framework of semivirial vanishing geometry.

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Amin Esfahani, Hichem Hajaiej, Yongming Luo, Linjie Song. 2023-05-31. On the focusing fractional nonlinear Schr\"{o}dinger equation on the waveguide manifolds. https://arxiv.org/abs/2305.19791

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