SOLITARY WAVE SOLUTIONS OF SOME CONFORMABLE TIME-FRACTIONAL COUPLED SYSTEMS VIA AN ANALYTIC APPROACH

2021 ◽  
Vol 21 (2) ◽  
pp. 487-502
Author(s):  
ANIQA ZULFIQAR ◽  
JAMSHAD AHMAD
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solution ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Coupled Systems ◽  
Conformable Derivative ◽  
Kdv Equations ◽  
Long Wave ◽  
Fractional Models ◽  
Coupled Kdv Equations

The main purpose of this research is to inquire the new solitary wave solution of the coupled time-fractional models to validate the influence and proficiency of the planned variational iteration method (VIM) using conformable derivative definition. Applications to four demanding nonlinear problems like Hirota-Satsuma coupled KdV equations, modified Boussinesq (MB) equation, approximate long wave (ALW) equation and Drinfeld-Sokolov-Wilson (DSW) equation demonstrate the efficiency and the robustness of the method. An analysis of the consequences with effects of relevant parameters and comparison with the exact solution presented with the help of graphs tables and gives the further understanding of numerical results by others. The convergence of the method is illustrated numerical and their physical significance is discussed

Solitary wave solutions, lump solutions and interactional solutions to the (3 + 1)-dimensional generalized B-type Kadomtsev-Petviashvili equation

2020 ◽  
Vol 34 (07) ◽  
pp. 2050053
Author(s):  
Min Gao ◽  
Hai-Qiang Zhang
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solution ◽  
Lump Solution ◽  
Solitary Wave Solutions ◽  
Bilinear Method ◽  
Long Wave ◽  
Petviashvili Equation ◽  
Dimensional Equation ◽  
Hirota Bilinear ◽  
Bkp Equation

In this paper, we investigate a [Formula: see text]-dimensional B-type Kadomtsev-Petviashvili (BKP) equation, which is a generalization of the [Formula: see text]-dimensional equation. Based on the Hirota bilinear method and the limit technique of long wave, we systematically construct a family of exact solutions of BKP equation including the [Formula: see text]-solitary wave solution, lump solution as well as interaction solution between lump waves and solitary waves.

scholarly journals Water Wave Solutions of the Coupled System Zakharov-Kuznetsov and Generalized Coupled KdV Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
A. R. Seadawy ◽  
K. El-Rashidy
Keyword(s):  
Solitary Wave ◽  
Traveling Wave Solutions ◽  
Coupled System ◽  
Solitary Wave Solutions ◽  
Coupled Partial Differential Equations ◽  
Extended Tanh Method ◽  
Kdv Equations ◽  
Wave Solutions ◽  
Tanh Method ◽  
Coupled Kdv Equations

An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solutions. The structures of the obtained solutions are distinct and stable.

scholarly journals A modification fractional variational iteration method for solving nonlinear gas dynamic and coupled KdV equations involving local fractional operators

2018 ◽  
Vol 22 (Suppl. 1) ◽  
pp. 165-175 ◽  
Author(s):  
Dumitru Baleanu ◽  
Hassan Jassim ◽  
Hasib Khan
Keyword(s):  
Iteration Method ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
New Technique ◽  
Transform Method ◽  
Variational Iteration ◽  
Kdv Equations ◽  
Gas Dynamic ◽  
Coupled Kdv Equations ◽  
A New Technique

In this paper, we apply a new technique, namely local fractional variational iteration transform method on homogeneous/non-homogeneous non-linear gas dynamic and coupled KdV equations to obtain the analytical approximate solutions. The iteration procedure is based on local fractional derivative and integral operators. This method is the combination of the local fractional Laplace transform and variational iteration method. The method in general is easy to implement and yields good results. Illustrative examples are included to demonstrate the validity and applicability of the new technique.

Time-Fractional Camassa–Holm Equation: Formulation and Solution Using Variational Methods

2013 ◽  
Vol 8 (4) ◽  
Author(s):  
Youwei Zhang
Keyword(s):  
Solitary Wave ◽  
Variational Methods ◽  
Iteration Method ◽  
Wave Solution ◽  
Solitary Wave Solution ◽  
Variational Iteration Method ◽  
Variational Technique ◽  
Holm Equation ◽  
Liouville Derivative ◽  
He’S Variational Iteration Method

This paper presents the formulation of the time-fractional Camassa–Holm equation using the Euler–Lagrange variational technique in the Riemann–Liouville derivative sense and derives an approximate solitary wave solution. Our results witness that He's variational iteration method was a very efficient and powerful technique in finding the solution of the proposed equation.

scholarly journals Comparative study of two techniques on some nonlinear problems based ussing conformable derivative

2020 ◽  
Vol 9 (1) ◽  
pp. 470-482
Author(s):  
Aniqa Zulfiqar ◽  
Jamshad Ahmad
Keyword(s):  
Nonlinear Partial Differential Equations ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Conformable Derivative ◽  
Transform Method ◽  
Fractional Equations ◽  
Differential Transform ◽  
Foam Drainage Equation

AbstractIn this paper, three eminent types of time-fractional nonlinear partial differential equations are considered, which are the fractional foam drainage equation, fractional Gardner equation, and fractional Fornberg–Whitham equation in the sense of conformable fractional derivative. The approximate solutions of these considered problems are constructed and discussed using the conformable fractional variational iteration method and conformable fractional reduced differential transform method. The conformable derivative is one of the admirable choices to handle nonlinear physical problems of different fields of interest. Comparisons of approximate solution obtained by two techniques, to each other and with the exact solutions are also presented and affirm that the considered methods are efficient and reliable techniques to study other nonlinear fractional equations and models in the sense of conformable derivative. To explain the effects of several parameters and variables on the movement, the approximate results are shown in tables and two-and three-dimensional surface graphs.

scholarly journals A Modified Equation Approach to Selecting a Nonstandard Finite Difference Scheme Applied to the Regularized Long Wave Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
E. Momoniat
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Solitary Wave ◽  
Nonlinear Term ◽  
Solitary Wave Solution ◽  
Finite Difference Schemes ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Modified Equation ◽  
Nonstandard Finite Difference

Two nonstandard finite difference schemes are derived to solve the regularized long wave equation. The criteria for choosing the “best” nonstandard approximation to the nonlinear term in the regularized long wave equation come from considering the modified equation. The two “best” nonstandard numerical schemes are shown to preserve conserved quantities when compared to an implicit scheme in which the nonlinear term is approximated in the usual way. Comparisons to the single solitary wave solution show significantly better results, measured in theL2andL∞norms, when compared to results obtained using a Petrov-Galerkin finite element method and a splitted quadratic B-spline collocation method. The growth in the error when simulating the single solitary wave solution using the two “best” nonstandard numerical schemes is shown to be linear implying the nonstandard finite difference schemes are conservative. The formation of an undular bore for both steep and shallow initial profiles is captured without the formation of numerical instabilities.

Sign in / Sign up

Export Citation Format

Share Document