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the variational approach in water waves
This post primarily introduces The Variational Approach and demonstrates how to employ the method to derive the Euler-Lagrange equations for the water wave equations
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The Equations for Water Waves
incompressible flow momentum equation and Surface of water waves and boundary condition and Variational Formulation
![](https://s2.loli.net/2024/05/30/ixRfWBONFQErVdn.jpg)
gravity wave and capillary wave
dispersion relation and solutions of the water wave equation incorporating surface tension
![](https://s2.loli.net/2024/03/25/gDq9kvS23EnjQtT.jpg)
water wave - stationary phase -final
Asymptotic expansion of analytic functions and contour integral
![](https://s2.loli.net/2024/03/05/CHydfMxtNKs9ja7.jpg)
water wave - stationary phase -2
asymptotic expansions for integrals
![](https://s2.loli.net/2024/03/03/EXY2Qox14mCFjqb.jpg)
water wave - stationary phase -1
asymptotic expansions and Abel's lemma
![](https://s2.loli.net/2024/03/03/FsZhOCefpgq3X12.jpg)
water wave -ray theory 3
hydrodynamic fundamental, small amplitude wave
![](https://s2.loli.net/2024/03/03/It6HlzWBFDO9dPY.jpg)
water wave -ray theory 2
hydrodynamic fundamental, small amplitude wave
![](https://s2.loli.net/2024/03/03/u6fHX1jzYpwDQU4.jpg)
water wave -ray theory 1
hydrodynamic fundamental, three conservation equations