This work deals with exact soliton solutions of the nonlinear long-short wave interaction system, utilizing two analytical methods. The system of coupled long-short wave interaction equations is studied by two analytical methods, namely, the generalized tan (ϕ/2)-expansion method and He's semi-inverse variational method, based upon the integration tools. Moreover, in this paper, we generalize two aforementioned methods which give new soliton wave solutions. Abundant exact traveling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play an important role in engineering and physics fields. By using these methods, exact solutions including the hyperbolic function solution, traveling wave solution, soliton solution, rational function solution, and periodic wave solution of this equation have been obtained. In addition, by using Matlab, some graphical simulations were done to see the behavior of these solutions.