On the analytical solutions of conformable time-fractional extended Zakharov–Kuznetsov equation through ( $$G'/G^{2}$$ G ′ / G 2 )-expansion method and the modified Kudryashov method

SeMA Journal ◽  
2018 ◽  
Vol 76 (1) ◽  
pp. 15-25 ◽  
Author(s):  
Muhammad Nasir Ali ◽  
M. S. Osman ◽  
Syed Muhammad Husnine
Keyword(s):  
Analytical Solutions ◽  
Expansion Method ◽  
Modified Kudryashov Method ◽  
Kudryashov Method

scholarly journals Abundant stable novel solutions of fractional-order epidemic model along with saturated treatment and disease transmission

Open Physics ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 843-852
Author(s):  
Mostafa M. A. Khater ◽  
Dianchen Lu ◽  
Samir A. Salama
Keyword(s):  
Fractional Order ◽  
Epidemic Model ◽  
Disease Transmission ◽  
Analytical Techniques ◽  
Expansion Method ◽  
Sis Epidemic Model ◽  
Modified Kudryashov Method ◽  
Simplest Equation Method ◽  
Kudryashov Method ◽  
Saturated Treatment

Abstract This article proposes and analyzes a fractional-order susceptible, infectious, susceptible (SIS) epidemic model with saturated treatment and disease transmission by employing four recent analytical techniques along with a novel fractional operator. This model is computationally handled by extended simplest equation method, sech–tanh expansion method, modified Khater method, and modified Kudryashov method. The results’ stable characterization is investigated through the Hamiltonian system’s properties. The analytical solutions are demonstrated through several numerical simulations.

New optical soliton solutions for Fokas–Lenells dynamical equation via two various methods

2021 ◽  
pp. 2150196
Author(s):  
Aly R. Seadawy ◽  
Khalid K. Ali ◽  
Jian-Guo Liu
Keyword(s):  
Schrodinger Equation ◽  
Dynamical Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Optical Soliton ◽  
Modified Kudryashov Method ◽  
Kudryashov Method ◽  
Spatio Temporal ◽  
Temporal Dispersal

In this paper, we examine the Fokas–Lenells equation (FLE) that depicts the promulgation of ultra-short pulsation in visual fibers while confirming the terms of the following asymptotic arrangement beyond those indispensable for the nonlinear Schrödinger equation. In addition the model includes both spatio–temporal dispersal and self-steepening terms. Then, we discuss deep visual solutions of the FLE via taking the modified Kudryashov method and the extended tanh expansion method.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

scholarly journals Searching for Analytical Solutions of the (2+1)-Dimensional KP Equation by Two Different Systematic Methods

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Yongyi Gu ◽  
Fanning Meng
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions ◽  
Rational Function ◽  
Analytical Solutions ◽  
Direct Methods ◽  
Expansion Method ◽  
Complex Method ◽  
Kp Equation ◽  
Extended Complex ◽  
Complex Nonlinear Systems

In this paper, we derive analytical solutions of the (2+1)-dimensional Kadomtsev-Petviashvili (KP) equation by two different systematic methods. Using the exp⁡(-ψ(z))-expansion method, exact solutions of the mentioned equation including hyperbolic, exponential, trigonometric, and rational function solutions have been obtained. Based on the work of Yuan et al., we proposed the extended complex method to seek exact solutions of the (2+1)-dimensional KP equation. The results demonstrate that the applied methods are efficient and direct methods to solve the complex nonlinear systems.

A STUDY ABOUT THE SOLUTIONS OF SCHRÖDINGER EQUATION WITH AN ASYMPTOTICALLY LINEAR POTENTIAL

1996 ◽  
Vol 11 (03) ◽  
pp. 207-209 ◽  
Author(s):  
ELSO DRIGO FILHO
Keyword(s):  
Quantum Mechanics ◽  
Schrödinger Equation ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Numerical Solutions ◽  
Expansion Method ◽  
Linear Potential ◽  
Asymptotically Linear

We determine the solutions of the Schrödinger equation for an asymptotically linear potential. Analytical solutions are obtained by superalgebra in quantum mechanics and we establish when these solutions are possible. Numerical solutions for the spectra are obtained by the shifted 1/N expansion method.

New soliton solutions for resonant nonlinear Schrödinger’s equation having full nonlinearity

2020 ◽  
Vol 34 (06) ◽  
pp. 2050032 ◽  
Author(s):  
Khalid K. Ali ◽  
Hadi Rezazadeh ◽  
R. A. Talarposhti ◽  
Ahmet Bekir
Keyword(s):  
Power Law ◽  
Soliton Solutions ◽  
Schrödinger’S Equation ◽  
Modified Kudryashov Method ◽  
Cubic Law ◽  
Kudryashov Method ◽  
Full Nonlinearity ◽  
Schrödinger's Equation ◽  
Nonlinear Schrodinger’S Equation ◽  
Nonlinear Schrödinger’S Equation

In this paper, we discuss deep visual solutions of resonant nonlinear Schrödinger’s equation having full nonlinearity via taking the modified Kudryashov method. There are four types of nonlinearity in this paper. They are quadratic-cubic law, anti-cubic law, cubic-quintic-septic law and triple-power law. By performing this algorithm, logarithmical and rational solitons are deduced.

Sign in / Sign up

Export Citation Format

Share Document