Further advanced investigation of the complex Hirota-dynamical model to extract soliton solutions

The complex Hirota-dynamical model (CHDM) has applications in the study of plasma physics, the investigation of fusion energy, astrophysical research, and space studies. The CHDM may also be used to investigate turbulent flows to study shocks and other nonlinear phenomena, and light waves venturing through the fibers. Nowadays, plasma physics, fusion energy, astrophysical research, and space studies are very interesting topics in the modern research. So, we need to shed light on this model as a good application in these fields. For deep investigation of these physical problems, we need to find their analytical solutions. In this study, we explore a variety of soliton solutions with different geometrical structures for the CHDM via the double variable expansion method. By means of this method, we have obtained three types of soliton solutions, namely, hyperbolic, trigonometric, and rational function solutions. The graphical interpretation of these solutions gives us some popular shapes such as singular-periodic, kink, bell, and singular shapes. The performed method is an efficient technique to execute and provides reliable analytical soliton solutions which are very important to further advanced investigation of the mention equation.