Highly dispersive optical soliton perturbation with Kudryashov’s sextic-power law nonlinear refractive index by semi-inverse variation

A single bright highly dispersive optical soliton solution is recovered from semi-inverse variational principle. The model contains six power law nonlinear terms that constitute self-phase modulation effect which was proposed by Kudryashov. The amplitude–width relation of the soliton was finally recovered by Cardano’s approach with appropriate and necessary constraints that are presented.