On the traveling wave solutions to the complex nonlinear second-order modified unstable (1+1)-dimensional Schrödinger equation

Abstract The present work applies the improved Bernoulli sub-equation function approach to efficiently generate traveling wave solutions for the (1+1)-dimensional second-order modified unstable complex nonlinear Schrödinger equation. The objective is to provide suitable particulars and semi-analytic solutions for the specified model. The proposed model is converted into a second-order nonlinear ordinary differential equation employing a traveling wave transformation. Several original wave solutions to the studied model are obtained, such as periodic, traveling waves, breather waves, and combined multiple forms. These solutions are expressed using a variety of complex exponential rational functions. Various solutions are shown using two- and three-dimensional graphics, using relevant arbitrary parameters to demonstrate their physical and dynamic consequences. Two-dimensional graphs are used to explain the impact of time evolution and its effectiveness in the structure of the solutions. The fact that this is the first time a particular mentioned model is examined using this semi-analytic method performs as proof of the work's originality.