Three-component coupled nonlinear Schrödinger equation: optical soliton and modulation instability analysis

This article studies the generalized (2 + 1)-dimensional shallow water equation by applying two recent analytical schemes (the extended simplest equation method and the modified Kudryashov method) for constructing abundant novel solitary wave solutions. These solutions describe the bidirectional propagating water wave surface. Some obtained solutions are sketched in two- and three-dimensional and contour plots for demonstrating the dynamical behavior of these waves along shallow water. The accuracy of the obtained solutions and employed analytical schemes is investigated using the evaluated solutions to calculate the initial condition, and then the well-known variational iterational (VI) method is applied. The VI method is one of the most accurate semi-analytical solutions, and it can be applied for high derivative order. The used schemes’ performance shows their effectiveness and power and their ability to handle many nonlinear evolution equations.

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Diverse novel analytical and semi-analytical wave solutions of the generalized (2+1)-dimensional shallow water waves model

Investigation of solitons and mixed lump wave solutions with (3+1)-dimensional potential-YTSF equation

The paper studies the optical solitons with coupled nonlinear Schrodinger system (CNLSS) that describes the propagation of waves in birefringence polarization-preserving fibers with four-wave mixin...

Investigation of optical solitons in birefringent polarization preserving fibers with four-wave mixing effect

Under investigation in this paper is the Ivancevic option pricing model. Based on trial function method, rogue wave and dark wave solutions are constructed. By means of symbolic computation, these analytical solutions are obtained with the Maple. Perturbation solutions are obtained through direct perturbation method. These results will enrich the existing literature of the Ivancevic option pricing model. Dynamical characteristics for rogue waves and dark waves are exhibited by using three-dimensional plots, curve plots, density plots and contour plots.

Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model

Graphene is one of the thinnest and hardest elastic nanoscale materials and has opened new horizons in the field of material science for its versatile applications. The thermophoretic motion system is under investigation which describes the propagation of solitons in substrate-supported graphene sheets. A test function of the extended three-soliton method is used to construct the new soliton solutions. The one-order and mixed-order solutions involving solitons and lump waves are constructed. The dynamical behaviour of solitons under reflection, periodic distribution and interaction is depicted. Moreover, the bright and mixed type lump wave soliton propagation and interaction are discussed.

Solitons and lump wave solutions to the graphene thermophoretic motion system with a variable heat transmission

The Nagumo equation describes a reaction–diffusion system in biology. Here, it is coupled to Burgers equation, via including convection, which is the Burgers–Nagumo equation (BNE). The first objective of this work is to present a theorem to reduce, approximately, the different versions of the fractional time derivatives (FTD) to an ordinary derivative (OD) with time dependent coefficients (non autonomous). The second objective is to find the exact solutions of the fractal and FTD-BNE is reduced to BNE with time dependent coefficient. Further similarity transformations are introduced. The unified and extended unified method are used to find the exact traveling waves solutions. Also, self-similar solutions are obtained. The novelties in this work are (i) reducing, via an analytic approximation, the different versions of FTD to non autonomous OD. (ii) Traveling and self-similar waves solutions of the FTD-BNE are derived. (iii) The effect of the order of fractional and fractal derivatives, on waves structure, are investigated. It is found that significant fractal effects hold for smaller order derivatives. While significant fractional effects hold for higher-order derivatives. It is found that, the solutions obtained show solitary wave, wrinkle soliton, solitons with double kinks or with spikes and undulated wave. Further It is shown that wrinkle soliton, with double kink configuration holds for smaller fractal order. While in the case of fractional derivative, this holds for higher orders. We mention that the results found here are completely new. Symbolic computations are carried by using Mathematica.

Mohammad Tantawy

Papers

Investigation of solitons and mixed lump wave solutions with (3+1)-dimensional potential-YTSF equation

Solitons and lump wave solutions to the graphene thermophoretic motion system with a variable heat transmission

Analytic Solutions of Fractal and Fractional Time Derivative-Burgers–Nagumo Equation