Traveling waves for a nonlinear Schrödinger system with quadratic interaction
Traveling waves for a nonlinear Schrödinger system with quadratic interaction
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DOI：
10.1007/s00208-022-02555-w
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发表时间：
2022-09
影响因子：
1.4
通讯作者：
Noriyoshi Fukaya;M. Hayashi;Takahisa Inui
中科院分区：
文献类型：
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作者：
Noriyoshi Fukaya;M. Hayashi;Takahisa Inui
研究了一类具有二次相互作用的非线性薛定谔方程组的行波解。对于非质量共振情形，系统不具有伽利略对称性，这是本文特别感兴趣的。我们用变分方法构造了行波解，发现对于非质量共振情形，存在与非线性椭圆方程“零质量”情形相对应的行波解.作为应用，我们还建立了振荡数据的新的全局存在性结果。我们的两个结果本质上都来自于系统中伽利略不变性的缺乏。
We study traveling wave solutions for a nonlinear Schrödinger system with quadratic interaction. For the non mass resonance case, the system has no Galilean symmetry, which is of particular interest in this paper. We construct traveling wave solutions by variational methods and see that for the non mass resonance case there exist specific traveling wave solutions which correspond to the solutions for “zero mass" case in nonlinear elliptic equations. We also establish the new global existence result for oscillating data as an application. Both of our results essentially come from the lack of Galilean invariance in the system.