NOTES ON PARA-HERMITE–EINSTEIN SPACETIMES

2012 ◽  
Vol 09 (01) ◽  
pp. 1250008 ◽  
Author(s):  
MACIEJ PRZANOWSKI ◽  
SEBASTIAN FORMAŃSKI ◽  
ADAM CHUDECKI
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Nonlinear Partial Differential Equation ◽  
Second Order ◽  
Einstein Metric ◽  
Partial Differential

Para-Hermite–Einstein spacetimes are considered. It is shown that any para-Hermite–Einstein metric is locally defined by one nonlinear partial differential equation of the second order for one function.

Frequencies of Axial Vibrations of the Beam

1997 ◽  
Author(s):  
Livija Cveticanin
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Analytical Methods ◽  
Nonlinear Partial Differential Equation ◽  
Second Order ◽  
Suggested Method ◽  
Longitudinal Vibrations ◽  
Partial Differential ◽  
Nonlinear Force ◽  
Axial Vibrations

Abstract In this paper the free longitudinal vibrations of the beam on which the strong nonlinear force of Winkler type acts are analyzed. The vibrations are described with a second order strong nonlinear partial differential equation. Various approximate analytical methods for solving this equation are developed in the paper. The lowest frequency of vibration obtained by the suggested method are compared. It can be seen that some differences appear.

scholarly journals EVOLUTION OF MODULATIONAL INSTABILITY IN TRAVELLING WAVE SOLUTION OF NON-LINEAR PARTIAL DIFFERENTIAL EQUATION

2020 ◽  
Vol 5 (1) ◽  
pp. 1-7
Author(s):  
Ram Dayal Pankaj ◽  
Arun Kumar ◽  
Chandrawati Sindhi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Wave Solution ◽  
Modulational Instability ◽  
Nonlinear Partial Differential Equation ◽  
Linear Partial Differential Equation ◽  
Travelling Wave ◽  
Travelling Wave Solution ◽  
Partial Differential ◽  
Jacobian Elliptic Functions

The Ritz variational method has been applied to the nonlinear partial differential equation to construct a model for travelling wave solution. The spatially periodic trial function was chosen in the form of combination of Jacobian Elliptic functions, with the dependence of its parameters

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