Traveling wave solutions of the generalized scale-invariant analog of the KdV equation by tanh-coth method

In this work, the generalized scale-invariant analog of the Korteweg-de Vries equation is studied. For the first time, the tanh-coth methodology is used to find traveling wave solutions for this nonlinear equation. The considered generalized equation is a connection between the well-known Korteweg-de Vries (KdV) equation and the recently investigated scale-invariant of the dependent variable (SIdV) equation. The obtained results show many families of solutions for the model, indicating that this equation also shares bell-shaped solutions with KdV and SIdV, as previously documented by other researchers. Finally, by executing the symbolic computation, we demonstrate that the used technique is a valuable and effective mathematical tool that can be used to solve problems that arise in the cross-disciplinary nonlinear sciences.