Cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended Jacobi’s elliptic function method

This paper studies two nonlinear coupled evolution equations. They are the Zakharov equation and the Davey–Stewartson equation. These equations are studied by the aid of Jacobi’s elliptic function expansion method and exact periodic solutions are extracted. In addition, the Zakharov equation with power law nonlinearity is solved by traveling wave hypothesis.

► Traveling wave soliton solutions were obtained for the Zakharov equation with power law nonlinearity.
► The extended Jacobi’s elliptic function method was used to integrate Zakharov equation and Davey–Stewartson equation.
► The constraint conditions were also obtained for the soliton solutions to exist.
► The numerical simulations are given.