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this paper, we study important Schr\\\"{o}dinger systems with linear and nonlinear couplings \\begin{equation}\\label{eq:diricichlet} \\begin{cases} -\\Delta u_1-\\lambda_1 u_1=\\mu_1 |u_1|^{p_1-2}u_1+r_1\\beta |u_1|^{r_1-2}u_1|u_2|^{r_2}+\\kappa (x)u_2~\\hbox{in}~\\mathbb{R}^N,\\\\ -\\Delta u_2-\\lambda_2 u_2=\\mu_2 |u_2|^{p_2-2}u_2+r_2\\beta |u_1|^{r_1}|u_2|^{r_2-2}u_2+\\kappa (x)u_1~ \\hbox{in}~\\mathbb{R}^N,\\\\ u_1\\in H^1(\\mathbb{R}^N), u_2\\in H^1(\\mathbb{R}^N),\\nonumber \\end{cases} \\end{equation} with the condition $$\\int_{\\mathbb{R}^N} u_1^2=a_1^2, \\int_{\\mathbb{R}^N} u_2^2=a_2^2,$$ where $N\\geq 2$, $\\mu_1","authors_text":"Zhaoyang Yun, Zhitao Zhang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2021-04-09T02:21:47Z","title":"Normalized solutions to Schr\\\"{o}dinger systems with linear and nonlinear 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