THE PERIODIC SOLUTIONS OF THE GBBM EQUATION

• Main Authors: Wen-Bin Lin, 林文彬
• Other Authors: Tai-Cheng Tso
• Format: Others
• Language: zh-TW
• Published: 2000
• Online Access: http://ndltd.ncl.edu.tw/handle/85892315749912629690

碩士 === 國立高雄師範大學 === 數學系 === 88 === In this paper, we use the Green function method to study periodic traveling wave solutions of the GBBM equation u_t+(f_0(u))_x-σu_{xxt}=0, where σ>0 is a constant and f_0(u) is a differentiable function in R. Through the construction of an explicit Green function it is shown that the perodic boundary-value problem for the periodic wave solution of the GBBM equation is equivalent to an integral equation with a symmetrical kernel which generates a compact operator in the space of periodic functions. Finally, this integral representation leads to the existence of a periodic traveling wave solution for an associated inhomogeneous GBBM equation u_t+(f_0(u))_x-σu_{xxt}=h(x-β_{0}t), where h is a given 2T-periodic function of ξ≡x-β_{0}t for some fixedβ_0>0.