scholarly journals Lie symmetry reductions and conservation laws for fractional order coupled KdV system

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Hong Guang Sun ◽  
Marzieh Azadi
Keyword(s):  
Conservation Laws ◽  
Fractional Order ◽  
Lie Symmetry ◽  
Theoretical Physics ◽  
Lie Symmetry Analysis ◽  
Kdv Equations ◽  
Ode System ◽  
Coupled Kdv Equations ◽  
Scientific Phenomena ◽  
New System

AbstractLie symmetry analysis is achieved on a new system of coupled KdV equations with fractional order, which arise in the analysis of several problems in theoretical physics and numerous scientific phenomena. We determine the reduced fractional ODE system corresponding to the governing factional PDE system.In addition, we develop the conservation laws for the system of fractional order coupled KdV equations.

scholarly journals Conservation Laws and Exact Series Solution of Fractional-Order Hirota-Satsoma Coupled KdV system by Symmetry Analysis

2021 ◽  
Author(s):  
Hemant Gandhi ◽  
Amit Tomar ◽  
Dimple Singh
Keyword(s):  
Conservation Laws ◽  
Fractional Order ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
Infinitesimal Generators ◽  
Coupled Equations ◽  
Fractional Differential ◽  
Power Series Technique ◽  
Series Technique

In this work, we investigated the invariance analysis of fractional-order Hirota-Satsoma coupled Korteveg-de-Vries (HSC-KdV) system of equations based on Riemann-Liouville (RL) derivatives. The Lie Symmetry analysis is considered to obtain infinitesimal generators; we reduced the system of coupled equations into nonlinear fractional ordinary differential equations (FODEs) with the help of Erdelyi’s-Kober (EK) fractional differential and integral operators. The reduced system of FODEs solved by means of the power series technique with its convergence. The conservation laws of the system constructed by Noether’s theorem.

Study on the Integrable Properties of Two Coupled KdV Equations

2011 ◽  
Vol 267 ◽  
pp. 683-692
Author(s):  
Li Yuan Zhang ◽  
Li Mei Cheng ◽  
Wei Yuan ◽  
Ruo Xia Yao
Keyword(s):  
Conservation Laws ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Symmetry And Conservation Laws ◽  
Lie Symmetry ◽  
Point Symmetry ◽  
Symmetry Groups ◽  
Kdv Equations ◽  
Generalized Symmetries ◽  
Coupled Kdv Equations

Two coupled KdV equations describing the atmospheric and oceanic phenomena are re-analyzed from the view points of Lie point symmetry, Lie symmetry groups, symmetry reductions, infinitely many generalized symmetries and conservation laws armed with the computer algebra system Maple. The results obtained in this paper show that the two coupled KdV equations are completely integrable in the sense of symmetry and conservation laws. Some results obtained by us are new and first reported here.

scholarly journals A Truncation Method for Solving the Time-Fractional Benjamin-Ono Equation

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Mohamed R. Ali
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Power Series ◽  
Fractional Order ◽  
Nonlinear Ordinary Differential Equation ◽  
Lie Symmetry ◽  
Series Method ◽  
Lie Symmetry Analysis ◽  
Power Series Method ◽  
Bo Equation

We deem the time-fractional Benjamin-Ono (BO) equation out of the Riemann–Liouville (RL) derivative by applying the Lie symmetry analysis (LSA). By first using prolongation theorem to investigate its similarity vectors and then using these generators to transform the time-fractional BO equation to a nonlinear ordinary differential equation (NLODE) of fractional order, we complete the solutions by utilizing the power series method (PSM).

scholarly journals New Soliton Solutions of Fractional Jaulent-Miodek System with Symmetry Analysis

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1001 ◽  
Author(s):  
Subhadarshan Sahoo ◽  
Santanu Saha Ray ◽  
Mohamed Aly Mohamed Abdou ◽  
Mustafa Inc ◽  
Yu-Ming Chu
Keyword(s):  
Conservation Laws ◽  
Fractional Differential Equations ◽  
Soliton Solutions ◽  
Logistic Function ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Fractional Differential ◽  
Physical Phenomena

New soliton solutions of fractional Jaulent-Miodek (JM) system are presented via symmetry analysis and fractional logistic function methods. Fractional Lie symmetry analysis is unified with symmetry analysis method. Conservation laws of the system are used to obtain new conserved vectors. Numerical simulations of the JM equations and efficiency of the methods are presented. These solutions might be imperative and significant for the explanation of some practical physical phenomena. The results show that present methods are powerful, competitive, reliable, and easy to implement for the nonlinear fractional differential equations.

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