WKB analysis for the three coupled long wave–short wave interaction equations

This paper is devoted to the WKB analysis of the three coupled long wave–short wave interaction (LSI for short) equations. We consider the zero-dispersion limit of the LSI for initial data with Sobolev regularity, before the shocks appear in the limit system. For the smooth solution, the limit system is given by the two fluids equations. The split-step Fourier method is also employed to justify the numerical simulation of the small dispersion limit.