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A new fractional-order derivative operator is presented and applied to nonlinear Sasa-Satsuma equation having Kerr nonlinearity law with third-order dispersion. Two novel families of singular, dark and bright soliton solutions for the fractional-order nonlinear Sasa-Satsuma equation were obtained by considering the modified simple equation method and the F-expansion method. Behavior of these soliton solutions are illustrated in 3d graphs, contour plots and 2d plots. Furthermore, periodic singular solutions of the equation are obtained by both analytical techniques. Optical type soliton solutions of the nonlinear Schrödinger equation is generated as well. To show out the behavior of the modulation gain spectra with the effects of the fractional derivative order, the linear stability technic was used. The effects of the fractional derivative order have been investigated in normal and anomalous dispersion regime associated to the Kerr nonlinearity effects. MI gain spectra were depicted by choosing adequate parameters of the fractional nonlinear Sasa-Satsuma equation. [ABSTRACT FROM AUTHOR]

In this paper, we implemented extended e x p - φ ξ -expansion method for some exact solutions of (3 + 1)-dimensional nonlinear Schrödinger equation (NLSE) and coupled nonlinear Schrodinger's equation. The solutions we obtained are hyperbolic, trigonometric and exponential solutions. We observed that these solutions provided the equations through Mathematica 11.2. Apart from that, we have shown the graphics performance of some of the solutions found. This method has been used recently to obtain exact traveling wave solutions of nonlinear partial differential equations. The results achieved in this study have been confirmed with computational software Maple or Mathematica by placing them back into NLFPDEs and found them correct. We posited that the approach is updated to be more pragmatic, efficacious, and credible and that we pursue more generalized precise solutions for traveling waves, like the solitary wave solutions. [ABSTRACT FROM AUTHOR]

A new local fractional-order derivative operator is introduced and the Lakshmanan–Porsezian–Daniel (LPD) model is interpreted via this operator. New analytical solutions to the LPD equation is presented by Jacobi elliptic functions and an anzätz method. The complex-valued LPD equation includes a nonlinear term which is considered from three different cases: Kerr, parabolic and anti-cubic law of nonlinearities. For each case, dark, bright, singular optical soliton solutions related with optical fibers are presented. Simulations representing behavior of these solutions for different parameter values are provided. [ABSTRACT FROM AUTHOR]

In this paper, we considered the nonlinear Schrodinger equation modeling cubic optical solitons in a polarization-preserving fiber with Kerr law. Using the improved t a n (φ / 2) -expansion method, a powerful and effective method, we constructed exact solutions including the hyperbolic function solution, the trigonometric function solution, the exponential solution and the rational solution with free parameters. The geometrical shapes for some of the obtained results are depicted for various choices of the free parameters that appear in the results. The obtained solutions are entirely new and can be considered as generalization of the existing results in the ordinary derivative case. [ABSTRACT FROM AUTHOR]

Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Correction to: Optical solitons of (3 + 1) dimensional and coupled nonlinear Schrodinger equations Correction to: https://doi.org/10.1007/s11082-022-03613-yhttps://doi.org/10.1007/s11082-022-0... The article with title "Optical solitons of (3 + 1) dimensional and coupled nonlinear Schrodinger equations" has been published twice with https://doi.org/10.1007/s11082-022-03613-y and https://doi.org/10.1007/s11082-022-03599-7. [Extracted from the article]