Highly dispersive optical solitons and conservation laws with Kudryashov’s sextic power–law of nonlinear refractive index

Abstract This current work addresses highly dispersive solitons in presence of Kudryashov’s sextic power law. Three independent approaches have made this retrieval possible. However, it is only with specific value of the power–law nonlinearity parameter, bright solitons emerge. Finally, conservation laws are presented for the model.