Owing to the inclusion of a small parameter (i.e., \(0<\varepsilon \ll {1}\) ) in the wave operator and initial velocity, the solution of the nonlinear Schrödinger equation with wave operator (NLSW) exhibits high oscillation in time, thereby posing significant challenges in constructing high-resolution numerical methods and establishing the uniform error estimates for the proposed methods. This paper introduces two novel exponential wave integrator Fourier pseudo-spectral methods (one is two-level implicit and time reversible, the other is three-level explicit) for solving the periodic boundary-initial value problem of the NLSW. A concise analysis establishes the uniform error estimates. Numerical experiments validate the uniform error estimates and efficiency of these two methods.
