Lie point symmetries, conservation laws, and analytical solutions of a generalized time-fractional Sawada–Kotera equation

Zou, Li; Yu, Zongbing; Tian, Shou‐Fu; Wang, Xiu‐Bin; Li, Jin

doi:10.1080/17455030.2018.1451666

Cited by 12 publications

(3 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also, we aimed to find the Lie symmetries for Equation (1) using the Lie group analysis. [37][38][39] Then, these symmetries are used to derive conservation laws 35,36,[40][41][42][43] for Equation (1) via formal Lagrangian. In addition, a reduced form of this equation is given by the similarity variables, which are obtained from the symmetries.…”

Section: Introductionmentioning

confidence: 99%

The time‐fractional generalized Z‐K equation: Analysis of Lie group, similarity reduction, conservation laws, and explicit solutions

Al-Denari

Ahmed

Tharwat

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we consider the three-dimensional non-linear time-fractional generalized Zakharov-Kuznetsov (Z-K) equation that describes the dust-ion acoustic solitary waves in a magnetized dusty plasma. Based on the definition of the Riemann-Liouville (R-L) fractional derivatives, the analysis of the Lie group method can be applied to find the symmetries for the considered equation. After that, these symmetries enable us to transform the equation under study into a two-dimensional non-linear ordinary differential equation of fractional order in the sense of ErdLélyi-Kober (E-K) fractional operator. Also, we obtain a set of new analytical solutions for the time-fractional generalized Z-K equation via the power series and the fractional sub-equation methods. Furthermore, we compute the conservation laws for this equation with a detailed derivation based on the formal Lagrangian.

show abstract

Section: Introductionmentioning

confidence: 99%

The time‐fractional generalized Z‐K equation: Analysis of Lie group, similarity reduction, conservation laws, and explicit solutions

Al-Denari

Ahmed

Tharwat

2022

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…Later, this method is applied to different versions of the (n + 1)-dimensional KP equation. In addition, some approaches have been used recently for the derivation of conservation laws and Lie symmetry analyzes for the fractional differential equations [31][32][33]. At the beginning of these approaches are the famous Noether theorem [34] and then the new method developed by Ibragimov [35].…”

Section: Introductionmentioning

confidence: 99%

New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics

et al. 2021

View full text Add to dashboard Cite

In this study, first, fractional derivative definitions in the literature are examined and their disadvantages are explained in detail. Then, it seems appropriate to apply the (G′G)-expansion method under Atangana’s definition of β-conformable fractional derivative to obtain the exact solutions of the space–time fractional differential equations, which have attracted the attention of many researchers recently. The method is applied to different versions of (n+1)-dimensional Kadomtsev–Petviashvili equations and new exact solutions of these equations depending on the β parameter are acquired. If the parameter values in the new solutions obtained are selected appropriately, 2D and 3D graphs are plotted. Thus, the decay and symmetry properties of solitary wave solutions in a nonlocal shallow water wave model are investigated. It is also shown that all such solitary wave solutions are symmetrical on both sides of the apex. In addition, a close relationship is established between symmetric and propagated wave solutions.

show abstract

“…A Crank-Nicolson Legendre spectral method was developed to solve the two-dimensional nonlinear time-fractional diffusion-wave equation [8]. Zou et al considered the following generalized time-fractional Sawada-Kotera equation [9]:…”

Section: Introductionmentioning

confidence: 99%

Lie Symmetry Analysis, Analytical Solution, and Conservation Laws of a Sixth-Order Generalized Time-Fractional Sawada-Kotera Equation

Yuhang

2019

Symmetry

View full text Add to dashboard Cite

To discuss the invariance properties of a sixth-order generalized time-fractional Sawada-Kotera equation, on the basis of the Riemann-Liouville derivative, the Lie point symmetry and symmetry reductions are derived. Then the power series theory is used to construct the exact power series solution of the equation. Finally, the conservation laws for a sixth-order generalized time-fractional Sawada-Kotera equation are computed.

show abstract

Lie point symmetries, conservation laws, and analytical solutions of a generalized time-fractional Sawada–Kotera equation

Cited by 12 publications

References 53 publications

The time‐fractional generalized Z‐K equation: Analysis of Lie group, similarity reduction, conservation laws, and explicit solutions

The time‐fractional generalized Z‐K equation: Analysis of Lie group, similarity reduction, conservation laws, and explicit solutions

New Solitary and Periodic Wave Solutions of (n + 1)-Dimensional Fractional Order Equations Modeling Fluid Dynamics

Lie Symmetry Analysis, Analytical Solution, and Conservation Laws of a Sixth-Order Generalized Time-Fractional Sawada-Kotera Equation

Contact Info

Product

Resources

About