Complete Classification and Nondegeneracy of $N$-Component Cubic Nonlinear Schrödinger System in $\mathbb{R}$

Yujin Guo, Yong Luo, Juncheng Wei

We study the one-dimensional cubic nonlinear Schrödinger system \[ u_i''+2\left(\sum_{k=1}^N u_k^2\right)u_i=-μ_i u_i \quad \mbox{in } \ \mathbb R,\ \ i=1,2,\cdots,N, \] where $u…