Soliton solutions of two-component Bose-Einstein condensates with Lee-Huang-Yang correction

This article selects the hyperbolic sine function as the trial wave function for the two-component Bose-Einstein condensate soliton solution with Lee-Huang-Yang (LHY) corrections. The Euler-Lagrange equation is derived by variational method, and the static soliton analytical solution is obtained by solving the time-independent Euler-Lagrange equation. The static soliton analytical solution is compared with the static soliton numerical solution. The results show that in the absence of the harmonic potential, the trial wave function provides a good approximation for the static soliton solution, in the presence of the harmonic potential, when $0<G<0.40,0<g_{ii}-g_{ij}<4.0$, the trial wave function also provides a good approximation for the static soliton solution.