Normalized ground state solutions of Schrödinger-KdV system in ${\mathbb{R}}^3$

In this paper, we study the coupled Schrödinger-KdV system \begin{align*} \begin{cases} -Δu +λ_1 u=u^3+βuv~~&$\text{in}$$\mathbb{R}$^{3}, \-Δv +λ_2 v=\frac{1}{2}v^2+\frac{1}{2}βu^2&$\text{in}$~~$\mathbb{R}$^{3} \end{cases} \end{align*} subject to the mass constraints \begin{equation*} \int_{$\mathbb{R}$^{3}}|u|^2 dx=a,\quad \int_{$\mathbb{R}$^{3}}|v|^2 dx=b, \end{equation*} where $a,b>0$ are given constants, $\beta >0$, and the frequencies ${\lambda }_1,{\lambda }_2$ arise as Lagrange multipliers. The system exhibits $L^2$-supercritical growth. Using a novel constraint minimization approach, we demonstrate the existence of a local minimum solution to the system. Furthermore, we establish the existence of normalized ground state solutions.