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This paper secures dark and singular resonant optical solitons that is studied with dual-power law nonlinearity and fractional temporal evolution. Khalil's conformable fractional derivative is put into perspective to retrieve these soliton solutions. The parameter restrictions for the existence of such solitons are also indicated. [ABSTRACT FROM AUTHOR]

In this paper, two distinct methods are applied to look for exact traveling wave solutions of the (4+1)-dimensional nonlinear Fokas equation, namely the modified simple equation method (MSEM) and the extended simplest equation method (ESEM). Some new exact traveling wave solutions involving some parameters are obtained. The solitary wave solutions can be extracted by assigning special values of these parameters. The obtained solutions show the simplicity and efficiency of the used approaches that can be applied for nonlinear equations as well as linear ones. [ABSTRACT FROM AUTHOR]

In this paper, the modified simple equation method (MSEM) is applied to construct exact solutions of the generalized ( 2 + 1 )-dimensional nonlinear evolution equations (NLEEs) involving parameters via the ( 2 + 1 )-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation, the ( 2 + 1 )-dimensional breaking soliton equation and the ( 2 + 1 )-dimensional Bogoyavlenskii’s breaking soliton equation. The solitary wave solutions are derived from the exact solutions by assigning special values of the parameters. [ABSTRACT FROM AUTHOR]