scholarly journals A Method of Solving Partial Differential Equations which have a general first Integral, applied to Equations of the Third Order with two Independent Variables

1876 ◽  
Vol s1-8 (1) ◽  
pp. 229-262
Author(s):  
H. W. Lloyd Tanner
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
First Integral ◽  
Third Order ◽  
Partial Differential ◽  
Independent Variables ◽  
The Third ◽  
Two Independent Variables

scholarly journals An integrable system of partial differential equations on the special linear group

2002 ◽  
Vol 44 (1) ◽  
pp. 83-93
Author(s):  
Peter J. Vassiliou
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Linear Group ◽  
Special Linear Group ◽  
Partial Differential ◽  
Special Linear ◽  
First Order ◽  
Independent Variables ◽  
Two Independent Variables

AbstractWe give an intrinsic construction of a coupled nonlinear system consisting of two first-order partial differential equations in two dependent and two independent variables which is determined by a hyperbolic structure on the complex special linear group regarded as a real Lie groupG. Despite the fact that the system is not Darboux semi-integrable at first order, the construction of a family of solutions depending.upon two arbitrary functions, each of one variable, is reduced to a system of ordinary differential equations on the 1-jets. The ordinary differential equations in question are of Lie type and associated withG.

scholarly journals Improvement of the Modified Decomposition Method for Handling Third-Order Singular Nonlinear Partial Differential Equations with Applications in Physics

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Nemat Dalir
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Differential Operators ◽  
Nonlinear Partial Differential Equations ◽  
Initial Value ◽  
Third Order ◽  
Partial Differential ◽  
The Third

The modified decomposition method (MDM) is improved by introducing new inverse differential operators to adapt the MDM for handling third-order singular nonlinear partial differential equations (PDEs) arising in physics and mechanics. A few case-study singular nonlinear initial-value problems (IVPs) of third-order PDEs are presented and solved by the improved modified decomposition method (IMDM). The solutions are compared with the existing exact analytical solutions. The comparisons show that the IMDM is effectively capable of obtaining the exact solutions of the third-order singular nonlinear IVPs.

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