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

Abstract

Abstract 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.