On the solution of time-fractional KdV–Burgers equation using Petrov–Galerkin method for propagation of long wave in shallow water

2018 ◽  
Vol 116 ◽  
pp. 376-380 ◽  
Author(s):  
A.K. Gupta ◽  
S. Saha Ray
Keyword(s):  
Galerkin Method ◽  
Shallow Water ◽  
Burgers Equation ◽  
Long Wave

scholarly journals Exact solutions and conservation laws for the modified equal width-Burgers equation

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 795-800 ◽  
Author(s):  
Chaudry Masood Khalique ◽  
Innocent Simbanefayi
Keyword(s):  
Conservation Laws ◽  
Burgers Equation ◽  
Expansion Method ◽  
Momentum Conservation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Lie Symmetry Method ◽  
Long Wave ◽  
Symmetry Method ◽  
Conservation Theorem

AbstractIn this paper we study the modified equal width-Burgers equation, which describes long wave propagation in nonlinear media with dispersion and dissipation. Using the Lie symmetry method in conjunction with the (G'/G)− expansion method we construct its travelling wave solutions. Also, we determine the conservation laws by invoking the new conservation theorem due to Ibragimov. As a result we obtain energy and linear momentum conservation laws.

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