A Study of Difference Between The Developing form of Boussinesq equation and Airy Wave
Zhang Yonggang
(Dept. of Mechanic Engineering, Shanghai Jiaotong University£©
Li Yucheng
(Dept. of Civil Engineering, Dalian University of Technology, Dalian£©

Abstract: In the paper, a new form of the Boussinesq equation is derived by the theory of potent function with method of recurrence formula. Developing tendency and different form of the Boussinesq equation may be discussed by setting up some parameters of the Boussinesq equation. For shallow water wave propagation, the developing tendency is to increase the range of the equation to fit water de pth. The range increased is made by the degree approximative of dispersion character istics of the Bou ssinesq equation to dispersion characteristic of Airy wave. The Boussinesq equa tion differs fram Airy wave is that Boussinesq equation incl udes the term of dispersion and Airy wave has not the dispersion charaterirtic term. Airy wave is approximate to only the largest term of long wave, although Ai ry wave has accurate solution of dispereion. So Airy wave has vary large limit in sim ulating water wave propagation.
Keywords: Boussinesq equation, Airy wave, Pade approxima te, nonlinear interaction.