Nonlocal symmetry analysis, explicit solutions and conservation laws for the fourth-order Burgers’ equation

2015 ◽  
Vol 81 ◽  
pp. 290-298 ◽  
Author(s):  
Gangwei Wang ◽  
A.H. Kara
Keyword(s):  
Conservation Laws ◽  
Fourth Order ◽  
Burgers Equation ◽  
Symmetry Analysis ◽  
Explicit Solutions ◽  
Nonlocal Symmetry

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.

Explicit Solutions and Conservation Laws of a Coupled Burgers’ Equation

2017 ◽  
Vol 72 (9) ◽  
pp. 789-793
Author(s):  
Bo Xue ◽  
Fang Li ◽  
Yihao Li ◽  
Mingming Sun
Keyword(s):  
Conservation Laws ◽  
Gauge Transformation ◽  
Darboux Transformation ◽  
Burgers Equation ◽  
Integrable Equation ◽  
Explicit Solutions ◽  
Spectral Problems ◽  
Coupled Burgers Equation

AbstractBased on the gauge transformation between the corresponding 3×3 matrix spectral problems, N-fold Darboux transformation for a coupled Burgers’ equation is constructed. Considering the N=1 case of the derived Darboux transformation, explicit solutions for the coupled Burgers’ equation are given and their figures are plotted. Moreover, conservation laws of this integrable equation are deduced.

scholarly journals Comments on the Paper “Lie Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation”

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 900
Author(s):  
Roman Cherniha
Keyword(s):  
Conservation Laws ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Explicit Solutions ◽  
Two Dimensional ◽  
Lie Symmetry Analysis ◽  
Huxley Equation

This comment is devoted to the paper “Lie Symmetry Analysis, Explicit Solutions, and Conservation Laws of a Spatially Two-Dimensional Burgers–Huxley Equation” (Symmery, 2020, vol.12, 170), in which several results are either incorrect, or incomplete, or misleading.

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