Exact Series Solutions and Conservation Laws of Time Fractional Three Coupled KdV System

2020 ◽  
pp. 15-25 ◽  
Author(s):  
Komal Singla ◽  
R. K. Gupta
Keyword(s):  
Conservation Laws ◽  
Series Solutions

Symmetry reductions, explicit solutions, convergence analysis and conservation laws via multipliers approach to the Chen–Lee–Liu model in nonlinear optics

2019 ◽  
Vol 33 (04) ◽  
pp. 1950035 ◽  
Author(s):  
Aliyu Isa Aliyu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Mustafa Bayram ◽  
Dumitru Baleanu
Keyword(s):  
Nonlinear Optics ◽  
Power Series ◽  
Conservation Laws ◽  
Convergence Analysis ◽  
Symmetry Analysis ◽  
Explicit Solutions ◽  
Series Solutions ◽  
Symmetry Reductions ◽  
Power Series Solutions

In this paper, symmetry analysis is performed for the nonlinear Chen–Lee–Liu equation (NCLE) arising in temporal pulses. New forms of explicit solutions of the equation are constructed using the optimal systems by applying the power series solutions (PSS) technique and the convergence of the PSS is investigated. Finally, the conservation laws (Cls) of the model is studied using the multiplier approach.

scholarly journals Some invariant solutions and conservation laws of a type of long-water wave system

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Xiangzhi Zhang ◽  
Yufeng Zhang
Keyword(s):  
Conservation Laws ◽  
Water Wave ◽  
Lax Pair ◽  
Wave System ◽  
Series Solutions ◽  
Invariant Solutions ◽  
Group Invariant ◽  
Generalized System ◽  
Group Invariant Solutions ◽  
Similarity Reductions

AbstractWe propose a generalized long-water wave system that reduces to the standard water wave system. We also obtain the Lax pair and symmetries of the generalized shallow-water wave system and single out some their similarity reductions, group-invariant solutions, and series solutions. We further investigate the corresponding self-adjointness and the conservation laws of the generalized system.

scholarly journals Exact Solutions and Conservation Laws of the Time-Fractional Gardner Equation with Time-Dependent Coefficients

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2434
Author(s):  
Ruixin Li ◽  
Lianzhong Li
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Lie Symmetry ◽  
Time Dependent ◽  
Series Solutions ◽  
Lie Symmetry Analysis ◽  
Gardner Equation ◽  
Power Series Solutions ◽  
Conservation Theorem

In this paper, we employ the certain theory of Lie symmetry analysis to discuss the time-fractional Gardner equation with time-dependent coefficients. The Lie point symmetry is applied to realize the symmetry reduction of the equation, and then the power series solutions in some specific cases are obtained. By virtue of the fractional conservation theorem, the conservation laws are constructed.

Lie symmetry analysis, explicit solutions and conservation laws of the time fractional Clannish Random Walker’s Parabolic equation

2020 ◽  
pp. 2150074
Author(s):  
Panpan Wang ◽  
Wenrui Shan ◽  
Ying Wang ◽  
Qianqian Li
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Vector Fields ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Series Solutions ◽  
Lie Symmetry Analysis ◽  
Similarity Reduction ◽  
Power Series Solutions ◽  
Conservation Theorem

In this paper, we mainly study the symmetry analysis and conservation laws of the time fractional Clannish Random Walker’s Parabolic (CRWP) equation. The vector fields and similarity reduction of the time fractional CRWP equation are obtained. In addition, based on the power series theory, a simple and effective approach for constructing explicit power series solutions is proposed. Finally, by use of the new conservation theorem, the conservation laws of the time fractional CRWP equation are constructed.

scholarly journals Conservation laws, analytical solutions and stability analysis for the time-fractional Schamel–Zakharov–Kuznetsov–Burgers equation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
O. H. EL-Kalaawy ◽  
S. M. Moawad ◽  
M. M. Tharwat ◽  
Rasha B. Al-Denari
Keyword(s):  
Stability Analysis ◽  
Conservation Laws ◽  
Burgers Equation ◽  
Fractional Operator ◽  
Lie Point Symmetries ◽  
Series Solutions ◽  
Trial Equation Method ◽  
Power Series Solutions ◽  
Symmetry Method ◽  
Similarity Reductions

Abstract In this paper, we consider the $(3+1)$ ( 3 + 1 ) -dimensional time-fractional Schamel–Zakharov–Kuznetsov–Burgers (SZKB) equation. With the help of the Riemann–Liouville derivatives, the Lie point symmetries of the $(3+1)$ ( 3 + 1 ) -dimensional time-fractional SZKB equation are derived. By applying the Lie point symmetry method as well as Erdélyi–Kober fractional operator, we get the similarity reductions of the time-fractional SZKB equation. Conservation laws of the time-fractional SZKB are constructed. Moreover, we obtain its power series solutions with the convergence analysis. In addition, the analytical solution is obtained by modified trial equation method. Finally, stability is analyzed graphically in different planes.

Symmetry reductions, exact solutions, stability analysis and conservation laws of time-fractional Sharma–Tasso–Olever equation

2019 ◽  
Vol 16 (06) ◽  
pp. 1950087
Author(s):  
Youwei Zhang
Keyword(s):  
Differential Equation ◽  
Conservation Laws ◽  
Group Analysis ◽  
Lie Group Analysis ◽  
Series Solutions ◽  
Analysis Method ◽  
Symmetry Reductions ◽  
Wave Solutions ◽  
Power Series Solutions ◽  
Detailed Derivation

In this paper, Lie group analysis method is applied to consider a vector field and symmetry reductions for time-fractional Sharma–Tasso–Olver equation, exact hyperbolic wave solutions, power series solutions and its convergence are investigated. Stability and boundedness analysis of trivial solution to the reduced ordinary differential equation is shown by constructing appropriate Lyapunov function. Conservation laws of the equation are well constructed with a detailed derivation making use of Noether’s operator.

scholarly journals Lie Symmetry Analysis, Conservation Laws, Power Series Solutions, and Convergence Analysis of Time Fractional Generalized Drinfeld-Sokolov Systems

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 874
Author(s):  
Selahattin Gülşen ◽  
Shao-Wen Yao ◽  
Mustafa Inc
Keyword(s):  
Power Series ◽  
Conservation Laws ◽  
Group Analysis ◽  
Nonlinear Ordinary Differential Equation ◽  
Series Solutions ◽  
Nonlinear Odes ◽  
Fractional Differential Operator ◽  
Exact Power ◽  
Power Series Solutions ◽  
Fractional Differential

In this work, we investigate invariance analysis, conservation laws, and exact power series solutions of time fractional generalized Drinfeld–Sokolov systems (GDSS) using Lie group analysis. Using Lie point symmetries and the Erdelyi–Kober (EK) fractional differential operator, the time fractional GDSS equation is reduced to a nonlinear ordinary differential equation (ODE) of fractional order. Moreover, we have constructed conservation laws for time fractional GDSS and obtained explicit power series solutions of the reduced nonlinear ODEs that converge. Lastly, some figures are presented for explicit solutions.

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