One- and two-soliton solutions to a new KdV evolution equation with nonlinear and nonlocal terms for the water wave problem

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• 作者：M. Fokou ; T. C. Kofane ; A. Mohamadou ; E. Yomba
• 关键词：Higher ; order KdV equation ; Soliton solutions ; Water wave problem ; Hirota’s bilinear method
• 刊名：Nonlinear Dynamics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：83
• 期：4
• 页码：2461-2473
• 全文大小：1,510 KB
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• 作者单位：M. Fokou (1) (2)
  T. C. Kofane (1) (2)
  A. Mohamadou (2) (3)
  E. Yomba (4)
  
  1. Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon
  2. Centre d’Excellence Africain en Technologies de l’Information et de la Communication, University of Yaounde I, P.O. Box 812, Yaoundé, Cameroon
  3. Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Maroua, P.O. Box 814, Maroua, Cameroon
  4. Department of Mathematics, California State University-Northridge, Northridge, CA, 91330-8313, USA
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

With the help of the Boussinesq perturbation expansion, a new basic equation describing the long, small-amplitude, unidirectional wave motion in shallow water with surface tension is derived to fourth order, namely a higher-order Korteweg–de Vries (KdV) equation. The procedure for deriving this equation assumes that the relation between the small parameter \(\alpha \), which measures the ratio of wave amplitude to undisturbed fluid depth, and the small parameter \(\beta \), which measures the square of the ratio of fluid depth to wave length, is taken in the form \(\beta = 0(\alpha ) = \varepsilon \), where \(\varepsilon \) is a small, dimensionless parameter which is the order of the amplitude of the motion. Hirota’s bilinear method is used to investigate one- and two-soliton solutions for this new higher-order KdV equation. Keywords Higher-order KdV equation Soliton solutions Water wave problem Hirota’s bilinear method