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

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.

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Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation

Open Physics ◽

10.1515/phys-2018-0042 ◽

2018 ◽

Vol 16 (1) ◽

pp. 302-310 ◽

Cited By ~ 21

Author(s):

Dumitru Baleanu ◽

Mustafa Inc ◽

Abdullahi Yusuf ◽

Aliyu Isa Aliyu

Keyword(s):

Conservation Laws ◽

Nonlinear Ordinary Differential Equation ◽

Lie Symmetry ◽

Symmetry Analysis ◽

Lie Point Symmetries ◽

Fractional Partial Differential Equations ◽

Lie Symmetry Analysis ◽

Kawahara Equation ◽

Power Series Technique ◽

Series Technique

AbstractIn this work, Lie symmetry analysis for the time fractional simplified modified Kawahara (SMK) equation with Riemann-Liouville (RL) derivative, is analyzed. We transform the time fractional SMK equation to nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries with a new dependent variable. In the reduced equation, the derivative is in the Erdelyi-Kober (EK) sense. We solve the reduced fractional ODE using a power series technique. Using Ibragimov’s nonlocal conservation method to time fractional partial differential equations, we compute conservation laws (Cls) for the time fractional SMK equation. Some figures of the obtained explicit solution are presented.

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

Symmetry ◽

10.3390/sym12061001 ◽

2020 ◽

Vol 12 (6) ◽

pp. 1001 ◽

Cited By ~ 1

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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Lie symmetry analysis, conservation laws and similarity reductions of Newell–Whitehead–Segel equation of fractional order

Journal of Geometry and Physics ◽

10.1016/j.geomphys.2018.10.002 ◽

2019 ◽

Vol 135 ◽

pp. 116-128 ◽

Cited By ~ 3

Author(s):

Elaheh Saberi ◽

S. Reza Hejazi ◽

Ahmad Motamednezhad

Keyword(s):

Conservation Laws ◽

Fractional Order ◽

Lie Symmetry ◽

Symmetry Analysis ◽

Lie Symmetry Analysis ◽

Similarity Reductions

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

Advances in Difference Equations ◽

10.1186/s13662-020-03149-z ◽

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.

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