| Abstract: | We study numerically the semi‐classical limit for three‐coupled long wave–short wave interaction equations. The Fourier–Galerkin semi‐discretization is proved to be spectrally convergent in an appropriate energy space. We propose a split‐step Fourier method in the semi‐classical regime with the discussion of the meshing strategy, which is necessary to obtain correct numerical solution. Plane wave solution with weak and strong initial phases, solitary wave solution and Gaussian solution are considered to investigate the semi‐classical limit. |
