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We report exact bright and dark soliton solution to the nonlinear evolutionequation derived by Moses and Wise [Phys. Rev. Lett. 97, 073903, (2006)] forcascaded quadratic media beyond the slowly varying envelope approximations. Theintegrability aspects of the model are addressed. The traveling wave hypothesisas well as the ansatz method is employed to obtain an exact 1-soliton solution.Both bright and dark soliton solutions are obtained. The correspondingconstraint conditions are obtained in order for the soliton solutions to exist.

Solitary wave solution to the nonlinear evolution equation in cascaded quadratic media beyond the slowly varying envelope approximations