scholarly journals Explicit solutions for a modified 2+1-dimensional coupled Burgers equation by using Darboux transformation

2017 ◽  
Vol 69 ◽  
pp. 15-21 ◽  
Author(s):  
Ting Su
Keyword(s):  
Darboux Transformation ◽  
Burgers Equation ◽  
Explicit Solutions ◽  
Coupled Burgers Equation

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.

Darboux transformation approach for two new coupled nonlinear evolution equations

2019 ◽  
Vol 34 (01) ◽  
pp. 2050004
Author(s):  
Dan Zhao ◽  
Zhaqilao
Keyword(s):  
Darboux Transformation ◽  
Evolution Equations ◽  
Burgers Equation ◽  
Nonlinear Evolution ◽  
Kdv Equation ◽  
Lax Pair ◽  
Nonlinear Evolution Equations ◽  
Coupled Equations ◽  
Covariant Property ◽  
Coupled Burgers Equation

A new coupled Burgers equation and a new coupled KdV equation which are associated with [Formula: see text] matrix spectial problem are investigated for complete integrability and covariant property. For integrability, Lax pair and conservation laws of the two new coupled equations with four potentials are established. For covariant property, Darboux transformation (DT) is used to construct explicit solutions of the two new coupled equations.

scholarly journals On Conformable Double Laplace Transform and One Dimensional Fractional Coupled Burgers' Equation

2019 ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Adem Kilicman
Keyword(s):  
Laplace Transform ◽  
Burgers Equation ◽  
Decomposition Methods ◽  
Laplace Transforms ◽  
Existence Condition ◽  
One Dimensional ◽  
Double Laplace Transform ◽  
Coupled Burgers Equation

This article deals with the conformable double Laplace transforms and their some properties with examples and also the existence Condition for the conformable double Laplace transform is studied. Finally, in order to obtain the solution of nonlinear fractional problems, we present a modified conformable double Laplace that we call conformable double Laplace decomposition methods (CDLDM). Then, we apply it to solve, Regular and singular conformable fractional coupled burgers equation illustrate the effectiveness of our method some examples are given.

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