In this paper, the authors prove that the solutions \(f_\pm(x,\lambda)\) of the equation \[ -y''+e^{ix}y+q(x)y=\lambda^2y,\quad x\in(-\infty,\infty) \] where q is a complex-valued function satisfying \[ \int_{-\infty}^\infty(1+|x|)|q(x)|dx<\infty, \] enjoy the equations \[ f_\pm(x,\lambda)=f_0(x,\pm\lambda)\pm\int_{x}^{\pm\infty}K^\pm(x,t)f_0(x,\pm\lambda)dt, \] where \(K^\pm(x,t)\) are continuous functions and satisfy \[ |K^\pm(x,t)|\leq(1/2)\sigma_0^\pm(((x+t)/2))e^{\sigma_1^\pm(x)}, K^\pm(x,x)=\pm(1/2)\int_{x}^{\pm\infty}q(t)dt. \]