Normalized ground state solutions of Schrodinger-KdV system in R3

In this paper, we study the coupled Schrodinger-KdV system -Delta u + lambda(1)u = u(3) + beta uv in R-3, -Delta v + lambda(2)v = 1/2v(2) + 1/2 beta u(2) in R-3 subject to the mass constraints integral(R3)vertical bar u vertical bar(2) dx=a, integral(R3)vertical bar v vertical bar(2) dx=b, 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 minimumsolution to the system. Furthermore, we establish the existence of normalized ground state solutions.