Normalized solutions for Schrödinger systems in dimension two

In this paper, we study the existence of normalized solutions to the following nonlinear Schrödinger systems with exponential growth{−Δu+λ1u=Hu(u,v),in R2,−Δv+λ2v=Hv(u,v),in R2,∫R2|u|2dx=a2,∫R2|v|2dx=b2, where a,b>0 are prescribed, λ1,λ2∈R and the functions Hu,Hv are partial derivatives of a Carathéodory function H with Hu,Hv satisfying exponential growth in R2. Our main result is totally new for the Schrödinger system in R2. Using the Pohozaev manifold and variational methods, we establish the existence of normalized solutions to the above problem.