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arXiv · 1810.01385

Remarks on solitary waves and Cauchy problem for a Half-wave-Schr\"{o}dinger equations

Yakine Bahri·Slim Ibrahim·Hiroaki Kikuchi
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Abstract

In this paper, we study the solitary wave and the Cauchy problem for Half-wave-Schr\"{o}dinger equations in the plane. First, we show the existence and orbital stability of the ground states. Secondly, we prove that traveling waves exist and converge to zero as the velocity tends to $1$. Finally, we solve the Cauchy problem for initial data in $L^{2}_{x}H^{s}_{y}(\mathbb{R}^{2})$, with $s>\frac{1}{2}$.

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Yakine Bahri, Slim Ibrahim, Hiroaki Kikuchi. 2018-10-02. Remarks on solitary waves and Cauchy problem for a Half-wave-Schr\"{o}dinger equations. https://arxiv.org/abs/1810.01385

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