Nonautonomous analysis of steady Korteweg-de Vries waves under nonlocalised forcing

PHYSICA D-NONLINEAR PHENOMENA

卷:285

Article

Balasuriya, Sanjeeva¹  Binder, Benjamin J.¹ 

[1] Univ Adelaide, Sch Math Sci, Adelaide, SA 5005, Australia

关键词: Nonautonomous dynamical systems;    Homoclinic trajectories;    KdV equation;    Free-surface flow;    Solitary waves;   

DOI  :  10.1016/j.physd.2014.07.001

来源: Elsevier

【 摘 要 】

Recently developed nonautonomous dynamical systems theory is applied to quantify the effect of bottom topography variation on steady surface waves governed by the Korteweg-de Vries (KdV) equation. Arbitrary (but small) nonlocalised bottom topographies are amenable to this method. Two classes of free surface solutions - hyperbolic and homoclinic solutions of the associated augmented dynamical system - are characterised. The first of these corresponds to near-uniform free-surface flows for which explicit formula are developed for a range of topographies. The second corresponds to solitary waves on the free surface, and a method for determining their number is developed. Formula for the shape of these solitary waves are also obtained. Theoretical free-surface profiles are verified using numerical KdV solutions, and excellent agreement is obtained. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free