论文标题
与二次相互作用的非线性Schrödinger系统的行进波
Traveling waves for a nonlinear Schrödinger system with quadratic interaction
论文作者
论文摘要
我们研究了具有二次相互作用的非线性Schrödinger系统的行驶波解决方案。对于非质量共振案例，该系统没有伽利亚对称性，这在本文中特别感兴趣。我们通过变异方法构建行进波解决方案，并看到对于非质量共振案例，存在特定的行动波解决方案，与非线性椭圆方程中的“零质量”案例的解决方案相对应。我们还建立了振动性数据的新全球存在结果。我们的两个结果基本上来自该系统中缺乏Galilean Invariance的结果。
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.
