Head-on Collision between Two mKdV Solitary Waves in a Two-Layer Fluid System

Zhu Yong

Volume 13 Issue 5

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Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(5): 389-399

Zhu Yong. Head-on Collision between Two mKdV Solitary Waves in a Two-Layer Fluid System[J]. Applied Mathematics and Mechanics, 1992, 13(5): 389-399.

Citation:

Zhu Yong. Head-on Collision between Two mKdV Solitary Waves in a Two-Layer Fluid System[J]. Applied Mathematics and Mechanics, 1992, 13(5): 389-399.

Citation:

Zhu Yong. Head-on Collision between Two mKdV Solitary Waves in a Two-Layer Fluid System[J]. Applied Mathematics and Mechanics, 1992, 13(5): 389-399.

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Head-on Collision between Two mKdV Solitary Waves in a Two-Layer Fluid System

Zhu Yong

Laboratory for Nonlinear Mechanics of Continuous Media, Inst. of Mech., CAS, Beijing

Received Date: 1991-04-26
Publish Date: 1992-05-15

Abstract

Abstract

In this paper, based on the equations presented in [2], the head-on collision between two solitary waves described by the modified KdV equation (the mKdVequation, for short) is investigated by using the reductive perturbation method combined with the PLK method.These waves propagate at the interface of a two-fluid system, in which the density ratio of the two fluids equals the square of the depth ratio of the fluids.The second order perturbation solution is obtained.It is found that in the case of disregarding the nonuniform phase shift, the solitary waves preserve their original profiles after collision, which agrees with Fornberg and Whitham's numerical result of overtaking collision[6] whereas after considering the nonuniform phase shift, the wave profiles may deform after collision.
- mKdV solitary wave,
- head-on collision,
- perturbation method

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References(6)

References

[1]	Mile,J.W.,Solitary waves,Ann.Rev.Fluid Mech.,12 (1980),11-43.
[2]	戴世强.两层流体界面上的孤立波,应用数学和力学,3(6)(1982),721-731
[3]	Gear,J.and R.Grimshaw,Weak and strong interaction between internal solitary waves,Studies in Appl.Math.,68 (1984),253-258.
[4]	Mirie,R.M.and C.H.Su,Internal solitary waves and their head-on collision,Part I,J.Fluid Mech.,147 (1984),213-231;part Ⅱ,Phys.Fluids,29 (1986),31-37.
[5]	戴世强,两个界而孤立波之间的迎撞,力学学报,6(1983),523-532
[6]	Fornberg,B.and G.B.Whitham,A numerical and theoretical study of certain nonlinear wave phenomena,Phil.Trans.R.Soc.London,289(1978),373-404．

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