For the three-component cubic NLS system on the line with ordered negative frequencies, all solutions are classified into explicit forms, two distinct classes of normalized solutions exist depending on the μ values, and the linearized operator is nondegenerate at every nontrivial solution.
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Classification and Nondegeneracy of Cubic Nonlinear Schr\"{o}dinger System in $\mathbb{R}$
For the three-component cubic NLS system on the line with ordered negative frequencies, all solutions are classified into explicit forms, two distinct classes of normalized solutions exist depending on the μ values, and the linearized operator is nondegenerate at every nontrivial solution.