Nonrelativistic limit of normalized solutions to a class of nonlinear Dirac equations

In this paper, we investigate the nonrelativistic limit of normalized solutions to a nonlinear Dirac equation as given below: { -ic3 & sum;k=1 alpha k partial derivative ku+mc2 beta u-Gamma & lowast;(K|u|kappa)K|u|kappa-2u-P|u|s-2u=omega u, integral(R3)|u|(2)dx=1 Here ,c>0 represents the speed of light, m>0 is the mass of the Dirac particle,omega is an element of Remerges as an indeterminate Lagrange multiplier,Gamma,K,Pare real-valued function defined onR3, also known as potential functions. Our research first confirms the presence of normalized solutions to the Dirac equation under high-speed light conditions. We then illustrate that these solutions converge to normalized ground states of nonlinear Schr & ouml;dinger equations, and wealsoshowuniformboundednessandexponentialdecayofthesesolutions.Ourresultsformthefirst discussion on nonrelativistic limit of normalized solutions to nonlinear Dirac equations. This not only aids in the study of normalized solutions of the nonlinear Schr & ouml;dinger equations ,but also physically explains that the normalized ground states of high-speed particles and low-speed motion particles are consistent