Analytic bounded travelling wave solutions of some nonlinear equations II
作者: Eugenia N. PetropoulouPanayiotis D. SiafarikasIoannis D. Stabolas
作者单位: 1Department of Engineering Sciences, Division of Applied Mathematics and Mechanics, University of Patras, 26500 Patras, Greece
2Department of Mathematics, University of Patras, 26500 Patras, Greece
刊名: Chaos, Solitons and Fractals, 2008, Vol.41 (2), pp.803-810
来源数据库: Elsevier Journal
DOI: 10.1016/j.chaos.2008.04.002
英文摘要: Abstract(#br)Using a functional analytic method, it is proven that an initial value problem for a general class of higher order nonlinear differential equations has a unique bounded solution in the Banach space H 1 ( Δ ) of analytic functions, defined in the open unit interval Δ = ( - 1 , 1 ) . This result is also used for the study of travelling wave solutions of specific nonlinear partial differential equations, such as the KdV equation, the compound KdV–Burgers equation, the Kawahara equation, the KdV–Burgers–Kuramoto–Sivashinsky equation and a 7 th order generalized KdV equation. For each one of these equations, it is proven that there are analytic, bounded travelling wave solutions in the form of power series which are uniquely determined once the initial conditions are given. The...
全文获取路径: Elsevier  (合作)
影响因子:1.246 (2012)

  • nonlinear 非线性的
  • travelling 移动
  • bounded 有界的