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The current study suggests a new generalisation of highly dispersive nonlinear Schrödinger-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. [ABSTRACT FROM AUTHOR]

This analysis utilizes the generalized Riccati simple equation method to construct nematicons in liquid crystals from its governing system. A new type of nonlinearity is studied for the first time in the context of liquid crystals. It is the nonlinear quadruple power law. The fractional version of the governed model, with conformable sense, is considered. With the aid of Mathematica, Bright, dark, and singular types of solutions are derived with the constraints guaranteeing their existence. Moreover, some obtained results are depicted to show the real physical characteristics of nematicons. The used method provides a powerful tool for extracting exact solitary wave solutions. By simple calculations, we show that the generalized Riccati simple equation method can be treated as a general case of the well-known simple equation, exp - φ (η) -expansion, and G ′ / G -expansion methods. [ABSTRACT FROM AUTHOR]

In this paper, we examined four different forms of generalized (2+1)-dimensional Boussinesq–Kadomtsev–Petviashvili (B-KP)-like equations. In this connection, an accurate computational method based on the Riccati equation called sub-equation method and its Bäcklund transformation is employed. Using this method, numerous exact solutions that do not exist in the literature have been obtained in the form of trigonometric, hyperbolic, and rational. These solutions are of considerable importance in applied sciences, coastal, and ocean engineering, where the B–KP-like equations modeled for some significant physical phenomenon. The graph of the bright and dark solitons is presented in order to demonstrate the influence of different physical parameters on the solutions. All of the findings prove the stability, effectiveness, and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

In the current analysis, the conformable generalized Kudryashov equation of pulses propagation with power non-linearity is processed. The considered higher order equation represents a generalized mathematical model of many well-known ones in nonlinear media. A variety of multiple kinks, bi-symmetry, periodic, singular, bright and dark optical solitons are extracted via the generalized Riccati equation mapping method. Basing on the Riccati differential equation, the theoretical algorithm extracts a number of empirical solutions that do not exist in the literature. The obtained results showed that the present technique is an effective and strong tool for solving nonlinear fractional partial differential equations and produces a very large number of solutions. [ABSTRACT FROM AUTHOR]

The conformable derivative and adequate fractional complex transform are implemented to discuss the fractional higher-dimensional Ito equation analytically. The Jacobi elliptic function method and Riccati equation mapping method are successfully used for this purpose. New exact solutions in terms of linear, rational, periodic and hyperbolic functions for the wave amplitude are derived. The obtained solutions are entirely new and can be considered as a generalization of the existing results in the ordinary derivative case. Numerical simulations of some obtained solutions with special choices of free constants and various fractional orders are displayed. [ABSTRACT FROM AUTHOR]