scholarly journals Solving Variable-Coefficient Fourth-Order ODEs with Polynomial Nonlinearity by Symmetric Homotopy Method

2018 ◽  
Vol 7 (2) ◽  
pp. 58
Author(s):  
Abdrhaman Mahmoud
Keyword(s):  
Fourth Order ◽  
Variable Coefficient ◽  
Homotopy Method ◽  
Polynomial Nonlinearity

scholarly journals Conservation Laws for a Variable Coefficient Variant Boussinesq System

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Ben Muatjetjeja ◽  
Chaudry Masood Khalique
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Conservation Laws ◽  
Fourth Order ◽  
Variable Coefficient ◽  
Boussinesq System ◽  
Order System ◽  
Conserved Quantities ◽  
Third Order ◽  
Partial Differential

We construct the conservation laws for a variable coefficient variant Boussinesq system, which is a third-order system of two partial differential equations. This system does not have a Lagrangian and so we transform it to a system of fourth-order, which admits a Lagrangian. Noether’s approach is then utilized to obtain the conservation laws. Lastly, the conservation laws are presented in terms of the original variables. Infinite numbers of both local and nonlocal conserved quantities are derived for the underlying system.

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