New generalised cubic-quintic-septic NLSE and its optical solitons

The current study suggests a new generalisation of highly dispersive nonlinear Schrodinger-type equation (NLSE) with perturbation terms. With polynomial refractive index, known by cubic-quintic-septic (CQS) law and Hamiltonian-type cubic perturbation terms, the new model includes eighth-order dispersion term. The generalised Riccati simplest equation method (RSEM) and the modified simplest equation method (MSEM) are successfully utilised to analytically process the fractional version of the considered NLSE. A diverse collection of bright, dark and singular optical solitons under some constraints, in hyperbolic, periodic and rational-exponential forms are derived. Graphical interpretations of some obtained solutions are displayed. The two considered schemes, with different algorithms, show an influential mathematical tool for processing nonlinear fractional evolution equations.

Automated summary

The current study presents a new generalisation of highly dispersive nonlinear Schrodinger-type equation with perturbation terms, including eighth-order dispersion term. The RSEM and MSEM methods are successfully utilised to process the fractional version of the considered NLSE, resulting in a diverse collection of optical solitons with graphical interpretations showing their properties. These schemes provide an influential mathematical tool for processing nonlinear fractional evolution equations.