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一阶非线性项、四阶色散项的Boussinesq类方程
引用本文:林建国,邱大洪.一阶非线性项、四阶色散项的Boussinesq类方程[J].力学学报,1998,30(5):531-539.
作者姓名:林建国  邱大洪
作者单位:大连理工大学海岸与近海工程国家重点实验室
摘    要:推导了由一阶色散项O(β2)表示的Bousinesq类方程,方程中保留了一阶非线性项O(α)及四阶色散项O(β8),其中α=A/h0,β=h0/L,A为特征波高,L为特征波长,h0为特征水深从理论上证明了Bousinesq改善型方程对色散性精度的提高,阐明了此类方程对色散项所保留的精度为O(β8),而并非是此类方程推导之初的假设为O(β2)这一点,将改变人们传统的认识

关 键 词:一阶非线性项  四阶色散项  B类方程  波浪理论

BOUSSINESQ TYPE EQUATIONS WITH FIRST ORDER OF NONLINEARITY AND FOURTH ORDER OF DISPERSION
Lin Jianguo,Qiu Dahong.BOUSSINESQ TYPE EQUATIONS WITH FIRST ORDER OF NONLINEARITY AND FOURTH ORDER OF DISPERSION[J].chinese journal of theoretical and applied mechanics,1998,30(5):531-539.
Authors:Lin Jianguo  Qiu Dahong
Abstract:In this paper, the Boussinesq-type equations with first-order O(α) of nonlinearity and fourth-order O(β 8) of dispersion is derived, in which, α=A/h 0 , β=h 0/L , A, L and h 0 is typical value of wave amplitude, wavelength and water depth By using the transforming velcity, the linear dispersion relation of our equations is consistent with fourth order pade approximation of the exact linear dispersion relation for Airy waves, this make the equations applicable to a wider rang...
Keywords:first  order of nonlinearity  fourth  order of dispersion  Boussinesq  type equations  
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