H. M. Jaradat

A New Simplified Bilinear Method for the N-Soliton Solutions for a Generalized FmKdV Equation with Time-Dependent Variable Coefficients

Abstract In this paper a generalized fractional modified Korteweg–de Vries (FmKdV) equation with time-dependent variable coefficients, which is a generalized model in nonlinear lattice, plasma physics and ocean dynamics, is investigated. With the aid of a simplified bilinear method, fractional transforms and symbolic computation, the corresponding N-soliton solutions are given and illustrated. The characteristic line method and graphical analysis are applied to discuss the solitonic propagation and collision, including the bidirectional solitons and elastic interactions. Finally, the resonance phenomenon for the equation is examined.

Symbolic Computation on Soliton Solutions for Variable-coefficient Quantum Zakharov-Kuznetsov Equation in Magnetized Dense Plasmas

Abstract The (3+1)-dimensional quantum Zakharov-Kuznetsov equations with variable coefficients have the applications to nonlinear ion-acoustic waves in dense magnetoplasmas. Via a simplified bilinear method and symbolic computation, we construct the multiple solitary wave solutions, analyze the elastic collisions with the constant and variable coefficients, and observe that solitons no longer keep rectilinear propagation and display different shapes because of the inhomogeneities of media. Then, a dense magnetoplasma consisting of electrons and singly charged ions is considered. The basic set of quantum hydrodynamic is reduced to the quantum Zakharov-Kuznetsov equation by using the reductive perturbation technique. Parametric analysis is carried out in order to illustrate that the soliton amplitude, width and velocity are affected by the quantum diffraction and obliqueness effect. Furthermore, propagation characteristics and interaction behaviors of the solitons are also discussed through the graphical analysis and the characteristic-line method.

An Analytical Scheme for Multi-order Fractional Differential Equations

In this work, on the basis of homotopy analysis method, we propose a numerical procedure for solving multi-order fractional differential equations by transforming the original multi-order fractional differential equation into a system of single-order equations. To our knowledge this paper presents the first viable numerical method for an analytic solution of multi-order fractional differential equations. This approach provides a simple way to ensure the convergence of series of solution so that one can always get accurate enough approximations.

C-class functions with new approach on coincidence point results for generalized \((\psi ,\varphi )\)-weakly contractions in ordered b-metric spaces

Abstract In this paper, by using the C-class functions and a new approach we present some coincidence point results for four mappings satisfying generalized

Solving system of DAEs by homotopy analysis method

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Applications of a simplified bilinear method to ion-acoustic solitary waves in plasma

(ψ,ϕ)-weakly contractive condition in the setting of ordered b-metric spaces. Also, an application and example are given to support our results.In this paper, by using the C-class functions and a new approach we present some coincidence point results for four mappings satisfying generalized \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}

Analytical solution of time-fractional Drinfeld-Sokolov-Wilson system using residual power series method

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