On group analysis, conservation laws and exact solutions of time-fractional Kudryashov–Sinelshchikov equation

2021 ◽  
Vol 40 (5) ◽  
Author(s):  
P. Prakash
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Group Analysis

Group formalism of Lie transformations, exact solutions and conservation laws of nonlinear time-fractional Kramers equation

2020 ◽  
Vol 17 (12) ◽  
pp. 2050190
Author(s):  
Zahra Momennezhad ◽  
Mehdi Nadjafikhah
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Group Analysis ◽  
Systematic Investigation ◽  
Analysis Method ◽  
Invariance Properties ◽  
Kramers Equation ◽  
Fractional Differential ◽  
Lie Transformations ◽  
Noether Operators

In this paper, we will concentrate on a systematic investigation of finding Lie point symmetries of the nonlinear [Formula: see text]-dimensional time-fractional Kramers equation via Riemann–Liouville and Caputo derivatives. By using the Lie group analysis method, the invariance properties and the symmetry reductions of the time-fractional Kramers equation are provided. It is shown that by using one of the symmetries of the underlying equation, it can be transformed into a nonlinear [Formula: see text]-dimensional fractional differential equation with a new dependent variable and the derivative in Erdélyi–Kober sense. Furthermore, we construct some exact solutions for the time-fractional Kramers equation using the invariant subspace method. In addition, adapting Ibragimov’s method, using Noether identity, Noether operators and formal Lagrangian, we construct conservation laws of this equation.

Group analysis, exact solutions and conservation laws of a generalized fifth order KdV equation

2016 ◽  
Vol 86 ◽  
pp. 8-15 ◽  
Author(s):  
Gangwei Wang ◽  
Abdul H. Kara ◽  
Kamran Fakhar ◽  
Jose Vega-Guzman ◽  
Anjan Biswas
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Group Analysis ◽  
Fifth Order

Lie symmetries, exact solutions and conservation laws of the Oskolkov–Benjamin–Bona–Mahony–Burgers equation

2019 ◽  
Vol 34 (01) ◽  
pp. 2050012 ◽  
Author(s):  
S. Saha Ray
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Vector Fields ◽  
Group Analysis ◽  
Nonlinear Ordinary Differential Equation ◽  
Analysis Method ◽  
Lie Symmetry Analysis ◽  
Similarity Reduction ◽  
Reduction Equation ◽  
Conservation Theorem

In this paper, the Oskolkov–Benjamin–Bona–Mahony–Burgers (OBBMB) equation has been investigated by Lie symmetry analysis. Lie group analysis method is implemented to derive the vector fields and symmetry reductions. The OBBMB equation has been reduced into nonlinear ordinary differential equation (ODE) by exploiting symmetry reduction method. Using the similarity reduction equation, the exact solutions are obtained by extended [Formula: see text]-method. Finally, the new conservation theorem proposed by Ibragimov has been utilized to construct the conservation laws of the aforesaid equation.

scholarly journals Exact Solutions and Conservation Laws of a (2+1)-Dimensional Nonlinear KP-BBM Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Khadijo Rashid Adem ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Solitary Waves ◽  
Lie Group ◽  
Group Analysis ◽  
Equation Method ◽  
Two Dimensional ◽  
Lie Group Analysis ◽  
Simplest Equation Method ◽  
Bbm Equation

In this paper, we study the two-dimensional nonlinear Kadomtsov-Petviashivilli-Benjamin-Bona-Mahony (KP-BBM) equation. This equation is the Benjamin-Bona-Mahony equation formulated in the KP sense. We first obtain exact solutions of this equation using the Lie group analysis and the simplest equation method. The solutions obtained are solitary waves. In addition, the conservation laws for the KP-BBM equation are constructed by using the multiplier method.

Conserved Quantities for the General Linear Heat Equation

2016 ◽  
pp. 4437-4439
Author(s):  
Adil Jhangeer ◽  
Fahad Al-Mufadi
Keyword(s):  
Evolution Equation ◽  
Heat Equation ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Approach ◽  
General Linear ◽  
Conserved Quantities ◽  
Linear Heat ◽  
The Family ◽  
Partial Lagrangian

In this paper, conserved quantities are computed for a class of evolution equation by using the partial Noether approach [2]. The partial Lagrangian approach is applied to the considered equation, infinite many conservation laws are obtained depending on the coefficients of equation for each n. These results give potential systems for the family of considered equation, which are further helpful to compute the exact solutions.

scholarly journals Exact Explicit Solutions and Conservation Laws for a Coupled Zakharov-Kuznetsov System

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Equation Method ◽  
Explicit Solutions ◽  
Simplest Equation Method ◽  
De Vries

We study a coupled Zakharov-Kuznetsov system, which is an extension of a coupled Korteweg-de Vries system in the sense of the Zakharov-Kuznetsov equation. Firstly, we obtain some exact solutions of the coupled Zakharov-Kuznetsov system using the simplest equation method. Secondly, the conservation laws for the coupled Zakharov-Kuznetsov system will be constructed by using the multiplier approach.

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