Standing waves of nonlinear Schrödinger equations with the gauge field
Standing waves of nonlinear Schrödinger equations with the gauge field
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DOI：
10.1016/j.jfa.2012.05.024
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发表时间：
2012-09
影响因子：
1.7
通讯作者：
Jaeyoung Byeon;Hyungjin Huh;Jinmyoung Seok
中科院分区：
文献类型：
--
作者：
Jaeyoung Byeon;Hyungjin Huh;Jinmyoung Seok
研究了具有规范场的非线性Schrödinger方程的驻波。将规范场a μ用复标量场φ表示得到的泛函应用变分方法，建立了驻波存在性的一些结果。通过建立一个新的Sobolev型不等式，证明了在一定参数范围内不存在驻波。
We study standing waves for nonlinear Schrödinger equations with the gauge field. Some existence results of standing waves are established by applying variational methods to the functional which is obtained by representing the gauge field Aμin terms of complex scalar field ϕ. We also show that there exists no standing wave for certain range of parameters by establishing a new inequality of Sobolev type.