Nonclassical Potential Symmetries and New Explicit Solutions of Burgers Equation

2005 ◽  
Vol 44 (1) ◽  
pp. 11-14 ◽  
Author(s):  
Mao-Chang Qin ◽  
Feng-Xiang Mei ◽  
Xue-Jun Xu
Keyword(s):  
Burgers Equation ◽  
Explicit Solutions ◽  
Potential Symmetries

Nonclassical Potential Symmetries and New Explicit Solutions of the Burgers Equation

2005 ◽  
Vol 60 (1-2) ◽  
pp. 17-22 ◽  
Author(s):  
Maochang Qin ◽  
Fengxiang Mei ◽  
Xuejun Xu
Keyword(s):  
Symmetry Group ◽  
Burgers Equation ◽  
Lie Symmetry ◽  
Explicit Solutions ◽  
Potential Symmetries ◽  
Potential Symmetry ◽  
Symmetry Generators

Several new nonclassical potential symmetry generators to the Burgers equation are derived. Some explicit solutions, which cannot be derived from the Lie symmetry group of Burgers or its adjoined equation, are obtained by using these nonclassical potential symmetry generators.

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.

Notes on the Lie Symmetry Exact Explicit Solutions for Nonlinear Burgers' Equation

2019 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
General Solution ◽  
Nonlinear Equation ◽  
Burgers Equation ◽  
Lie Symmetry ◽  
Numerical Calculations ◽  
Explicit Solutions ◽  
Research Article ◽  
Original Works

In light of Liu et al.'s original works, this research article revisits the solution of Burgers's nonlinear equation. The researcher found two exact and explicit solutions for groups $G_4$ and $G_6$, as well as a general solution. Their applications were conducted by using numerical calculations.

New explicit solutions of the Burgers equation

2006 ◽  
Vol 48 (1-2) ◽  
pp. 91-96 ◽  
Author(s):  
Maochang Qin ◽  
Fengxiang Mei ◽  
Guihong Fan
Keyword(s):  
Burgers Equation ◽  
Explicit Solutions
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