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

Highly Dispersive Optical Solitons in Absence of Self-Phase Modulation by Laplace-Adomian Decomposition

This article studies highly dispersive optical solitons without of self-phase modulation effect. The numerical algorithm implemented in this work is Laplace-Adomian decomposition method. Both bright and dark solitons are addressed. The error measure for the adopted scheme is impressively low

Highly Dispersive Optical Solitons with Four Forms of Self-Phase Modulation

This paper implements the enhanced Kudryashov approach to retrieve highly dispersive optical solitons and study it with four nonlinear forms. These are the power law, generalized quadratic-cubic law, triple-power law, and the generalized non-local law. This approach reveals bright and singular optical solitons along with the respective parameter constraints