A new sensitive visualization, solitary wave profiles and conservation laws of ion sound waves arising in plasma

The current study covers the traveling wave structures of a fourth-order nonlinear symmetric regularized long-wave (SRLW) equation which emerges in a few actual applications incorporating particle sound waves in plasma using the new extended direct algebraic method. This model depicts nonlinear particle acoustic and space-charge waves. This model admits the two-dimensional Lie algebra. We have computed the optimal system and reduced our given model corresponding to each element of the optimal system. After that, by using a proposed method, we obtained the solitary wave profiles of the model under investigation. By using the concept of nonlinear self-adjointness, we have shown that our given model is not self-adjoint. Moreover, we have computed the conserved quantities corresponding to each element of the Lie algebra. The obtained solutions are in different classes of solitary wave solutions with dark, combined dark-bright, singular, periodic-singular, combined dark-singular, combined singular, dark-singular combo solitons, and rational solutions. Furthermore, existing constraints for the resultant solutions are reported. Also, a graphical interpretation of some particular solutions is shown by considering the specific values of the parameters. In the end, the sensitive visualization of the model is done by considering different initial states. We are confident that these outstanding results will offer insightful information and further the investigation of other evolutionary mechanisms connected to the equation under study.