Abstract
In this paper, the rational sine–cosine and rational sinh–cosh methods are applied in extracting some properties of nonlinear Phi-four and Gross–Pitaevskii equations. The singular periodic wave solutions, dark soliton solutions and hyperbolic function solutions are reported. The solitary waves are observed from the traveling waves under the values of the parameters. Modulation instability analysis is also observed in various simulations. We also plot to observe the wave distributions of parameters of stability in 2D and 3D visuals via package program.