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  • 标题:Existence of periodic traveling wave solution to the forced generalized nearly concentric Korteweg-de Vries equation
  • 本地全文:下载
  • 作者:Kenneth L. Jones ; Xiaogui He ; Yunkai Chen
  • 期刊名称:International Journal of Mathematics and Mathematical Sciences
  • 印刷版ISSN:0161-1712
  • 电子版ISSN:1687-0425
  • 出版年度:2000
  • 卷号:24
  • 期号:6
  • 页码:371-377
  • DOI:10.1155/S0161171200004336
  • 出版社:Hindawi Publishing Corporation
  • 摘要:

    This paper is concerned with periodic traveling wave solutions of the forced generalized nearly concentric Korteweg-de Vries equation in the form of ( u η + u / ( 2 η ) + [ f ( u ) ] ξ + u ξ ξ ξ ) ξ + u θ θ / η 2 = h 0 . The authors first convert this equation into a forced generalized Kadomtsev-Petviashvili equation, ( u t + [ f ( u ) ] x + u x x x ) x + u y y = h 0 , and then to a nonlinear ordinary differential equation with periodic boundary conditions. An equivalent relationship between the ordinary differential equation and nonlinear integral equations with symmetric kernels is established by using the Green's function method. The integral representations generate compact operators in a Banach space of real-valued continuous functions. The Schauder's fixed point theorem is then used to prove the existence of nonconstant solutions to the integral equations. Therefore, the existence of periodic traveling wave solutions to the forced generalized KP equation, and hence the nearly concentric KdV equation, is proved.

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