Nonlinear Self-Adjointness and Conservation Laws of KdV Equation with Linear Damping Force

2017 ◽  
Vol 5 (3) ◽  
pp. 89-94 ◽  
Author(s):  
Muhammad Nasir Ali ◽  
Shahid Ali ◽  
Syed Muhammad Husnine ◽  
Turgut Ak
Keyword(s):  
Conservation Laws ◽  
Kdv Equation ◽  
Damping Force ◽  
Linear Damping

The Analysis of Automotive Door Seal Energy Consumption

2011 ◽  
Vol 80-81 ◽  
pp. 714-718
Author(s):  
Yun Kai Gao ◽  
Da Wei Gao
Keyword(s):  
Energy Consumption ◽  
Elastic Force ◽  
Bernoulli Equation ◽  
Analysis Model ◽  
Damping Force ◽  
Total Energy Consumption ◽  
Linear Elastic ◽  
Non Linear ◽  
Linear Damping ◽  
Simplified Analysis

The seal deformation of automotive door is caused by the door compression forces, including non-linear elastic force and non-linear damping force. The working principles of them are analyzed and a new simplified analysis model is built. Based on the Bernoulli equation and the law of conservation of mass, the mathematical models are established to calculate energy consumption of the seal system. According to the analysis results, the energy consumption of non-linear elastic force and non-linear damping force are respectively 84% and 16% of the total energy consumption of the seal system. At last, the calculation data is compared with the test data and the error is less than 5%, so the calculation method proposed in this paper is observed to be accurate.

scholarly journals Lie symmetries, conservation laws and exact solutions of a generalized quasilinear KdV equation with degenerate dispersion

2020 ◽  
Vol 13 (10) ◽  
pp. 2691-2701
Author(s):  
María-Santos Bruzón ◽  
◽  
Elena Recio ◽  
Tamara-María Garrido ◽  
Rafael de la Rosa
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Kdv Equation ◽  
Lie Symmetries

Some conservation laws for a forced KdV equation

2012 ◽  
Vol 13 (6) ◽  
pp. 2692-2700 ◽  
Author(s):  
M.L. Gandarias ◽  
M.S. Bruzón
Keyword(s):  
Conservation Laws ◽  
Kdv Equation

scholarly journals Self-Adjointness and Conservation Laws of Frobenius Type Equations

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1987
Author(s):  
Haifeng Wang ◽  
Yufeng Zhang
Keyword(s):  
Conservation Laws ◽  
Burgers Equation ◽  
Kdv Equation ◽  
The Self ◽  
Kp Equation ◽  
Commutative Subalgebra ◽  
Kompaneets Equation ◽  
Dym Equation ◽  
Harry Dym Equation

The Frobenius KDV equation and the Frobenius KP equation are introduced, and the Frobenius Kompaneets equation, Frobenius Burgers equation and Frobenius Harry Dym equation are constructed by taking values in a commutative subalgebra Z2ε in the paper. The five equations are selected as examples to help us study the self-adjointness of Frobenius type equations, and we show that the first two equations are quasi self-adjoint and the last three equations are nonlinear self-adjointness. It follows that we give the symmetries of the Frobenius KDV and the Frobenius KP equation in order to construct the corresponding conservation laws.

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