Algebraic Solitary Waves in Stratified Fluids
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概要
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By using nonlinear perturbation method a time-dependent equation is derived which governs internal waves in stratified fluids of great depth. The resultant equation takes the following form: (∂u)/(∂t)+au(∂u)/(∂x)-β(∂^2)/(∂x^2)〓(u)=0, where 〓 denotes Hilbert transform of u. The equation admits exact solutions representing 'algebraic' solitary waves and nonlinear periodic waves, both of which were first obtained by Benjamin. It is found that the equation yields the time-invariant quantities such as ∫^∞_<-∞>udx, ∫^∞_<-∞>u^2dx, ∫^∞_<-∞>{u^3/3+(β/α)∂u/∂x〓(u)}dx and ∂∫^∞_<-∞>xudx/∂t. Based upon these conservation laws, break up of an initial Lorentzian pulse into two 'algebraic' solitary waves is discussed to predict the amplitude of emergent 'algebraic' solitrary waves.
- 1975-10-15
著者
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ONO Hiroaki
Department of Liberal Arts, Osaka Technical College
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Ono Hiroaki
Department Of Liberal Arts And Science Setsunan University
関連論文
- Algebraic Solitary Waves in Stratified Fluids
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