Abstract
In this paper, we study a nonlinear coupled system of partial differential equations which describe the resonance interactions between the long wave and the short wave (the LS type system). This system was first derived by Djordjevic and Redekopp. The semi-inverse variational principle and the first integral method as two main approaches are applied to this system. The former method yielded solitary wave solutions while the second approach resulted in shock wave solutions, plane wave solutions and singular periodic solutions. Finally, the traveling wave hypothesis is also applied to the LS wave equation in a generalized form where nonlinearity is extended to power law, and consequently a single solitary wave solution is formally derived. The special case, when power law nonlinearity parameter is relaxed to unity, is also included.