Novel optical structures for the cubic-quartic nonlinear Schrödinger equation: Analytical and numerical perspectives

The current paper uses both analytical and numerical approaches to explore the cubic-quartic nonlinear Schrödinger model governed by the Kerr law. For the analytical analysis, we employ the addendum to Kudryashov's method that yields several intriguing soliton solutions, including bright, singular, and bright-singular combos, which have potential applications in optoelectronics. In the numerical investigation, we adopt an enhanced numerical method that is based on the classical Adomian method. Certainly, this numerical scheme effectively validates the exactness of analytical solutions with an elevated precision. Finally, we provide certain assessment tables and graphical representations to supplement the findings of the study. In the end, the study recommends extending the findings of the present examination to various realms of complex-valued evolution equations, including higher-order models of complex power law nonlinearities among others.