scholarly journals Imaging Noise Suppression: Fourth-Order Partial Differential Equations and Travelling Wave Solutions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2019
Author(s):  
Sameerah Jamal
Keyword(s):  
Fourth Order ◽  
Noise Suppression ◽  
Linear Equations ◽  
Travelling Wave ◽  
Order Partial Differential Equation ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Total Variation Norm ◽  
Wave Solutions ◽  
Variation Norm

In this paper, we discuss travelling wave solutions for image smoothing based on a fourth-order partial differential equation. One of the recurring issues of digital imaging is the amount of noise. One solution to this is to minimise the total variation norm of the image, thus giving rise to non-linear equations. We investigate the variational properties of the Lagrange functionals associated with these minimisation problems.

scholarly journals Travelling Wave Solutions to the Benney-Luke and the Higher-Order Improved Boussinesq Equations of Sobolev Type

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Ömer Faruk Gözükızıl ◽  
Şamil Akçağıl
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boussinesq Equation ◽  
Boussinesq Equations ◽  
Travelling Wave ◽  
Higher Order ◽  
Sobolev Type ◽  
Travelling Wave Solutions ◽  
Partial Differential ◽  
Wave Solutions

By using the tanh-coth method, we obtained some travelling wave solutions of two well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation and the higher-order improved Boussinesq equation. We show that the tanh-coth method is a useful, reliable, and concise method to solve these types of equations.

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