Remarks on solitary waves and Cauchy problem for Half-wave-Schrodinger equations
Remarks on solitary waves and Cauchy problem for Half-wave-Schrodinger equations
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孤立波与半波薛定谔方程柯西问题的评述
DOI：
10.1142/s0219199720500583
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发表时间：
2020
影响因子：
1.6
通讯作者：
Kikuchi Hiroaki
中科院分区：
文献类型：
--
作者：
Bahri Yakine;Ibrahim Slim;Kikuchi Hiroaki
本文研究了平面上Half-wave-Schrödinger方程Cauchy问题的孤波解。首先，我们证明了基态的存在性和轨道稳定性。其次，证明了给定任意速度时，行波解存在，且随速度趋于收敛于零波。最后，我们解决了初始数据的柯西问题。这个关键的问题仍然是一个有趣的悬而未决的问题。
In this paper, we study solitary wave solutions of the Cauchy problem for Half-wave-Schrödinger equation in the plane. First, we show the existence and the orbital stability of the ground states. Second, we prove that given any speed, traveling wave solutions exist and converge to the zero wave as the velocity tends to. Finally, we solve the Cauchy problem for initial data in, with. The critical casestill stands as an interesting open problem.