This article deals with the new solitons and other solutions to the modified nonlinear Schrödinger equation (MNLSE) that represents the propagation of rogue waves in deep water. The solutions are achieved in the shape of trigonometric and hyperbolic functions as well as solitary wave solutions by the mean of extended sinh-Gordon equation expansion and (G′G2)-expansion function methods. Furthermore, the singular periodic wave solutions are obtained and the constraint conditions for the existence of soliton solutions are also listed. We also plot 3D graphs for a better explanation of the achieved solutions by choosing the appropriate values of the parameters involved in solutions. We can assert from the obtained results that the applied techniques are simple, vibrant, and quite well, and will be helpful tool for addressing more highly nonlinear issues in various of fields, especially in ocean and coastal engineering. Furthermore, our findings are first step toward understanding the structure and physical behavior of complicated structures. We anticipate that our results will be highly valuable in better understanding the waves that occur in the ocean. We feel that this work is timely and will be of interest to a wide spectrum of experts working on ocean engineering models.