On the study of analytical soliton solutions and interaction aspects to the Estevez-Mansfield-Clarkson equation arising in diversity of fields

Abstract The beta fractional form of the Estevez-Mansfield-Clarkson equation is under consideration and this study is done with the assistance of methods such as modified F-expansion method and the logarithmic transformation. A variety of analytical solutions like bright, dark, mixed, singular, bright-dark, and combined solitons are extracted. Moreover, multi waves structures, interaction with double exponential form, breather waves, mixed type solutions as well as periodic cross kink solutions have been analyzed. The governing equation is converted into an ordinary differential equation by employing an appropriate wave transformation with the β -derivative in order to achieve the desired solutions. The applied approaches have substantial computational capability, enabling them to efficiently address exact solutions with high accuracy in these systems. The results indicate that the equation under investigation theoretically contains a substantial number of soliton solution structures. Additionally, in order to examine the behaviors of the solutions at various parameter values, we plot a variety of graphs that incorporate pertinent parameters. The results of this study have the potential to improve understanding of the nonlinear dynamic characteristics displayed by the specified system and to confirm the effectiveness of the techniques that have been implemented.