Qualitative Theory of Dynamical Systems

, Volume 17, Issue 1, pp 103–122 | Cite as

Head-on Collision Between Two Hydroelastic Solitary Waves in Shallow Water

  • M. M. Bhatti
  • D. Q. LuEmail author


A comprehensive theoretical study on the head-on collision between two solitary waves in a thin elastic plate floating on an inviscid fluid of finite depth is investigated analytically by means of a singular perturbation method. The effects of plate compression are also taken into account. The Poincaré–Lighthill–Kuo method has been used to derive the solution up to the fourth order of the resulting nonlinear differential equation, which in principle gives the asymptotic series solution. It is found that after collision, both the hydroelastic solitary waves preserves their original shape and positions. However a collision does have imprints on colliding waves with non-uniform phase shift up to the third order which creates tilting in the wave profile. Maximum run-up amplitude, wave speed, phase shift and distortion profile have also been calculated and plotted for two colliding solitary waves.


Head-on collision Solitary waves Thin elastic plate Perturbation solutions Compressive force 



This research was sponsored by the National Natural Science Foundation of China under Grant No. 11472166. The authors are indebted to the reviewer for his/her critical comments that led to improvement in the work.


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© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina
  2. 2.Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai UniversityShanghaiChina

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