Peakons and solitary shock waves in compressible hyperelastic rods

Hui hui Dai

Peakons and solitary shock waves in compressible hyperelastic rods

City University of Hong Kong

Research output: Chapters, Conference Papers, Creative and Literary Works › RGC 32 - Refereed conference paper (with host publication) › peer-review

Abstract

The model equation (KdV equation) is used for long finite-but-small amplitude waves. However, the KdV equation does not have a solitary shock wave as its solution. A new type of equation is derived as the model equation, u_τ+ζ₁uu_ξ+σ₁u_ξξτ = σ₂(2u_ξu_ξξ+uu_ξξξ) (1), where ζ₁, σ₁2 are constant coefficients related to material constants. Equation (1) is rescaled to yield u_t+3uu_x-u_xxt = γ2u_xu_xx+uu_xxx) (2). Equation (2) is reduced to a system of ordinary differential equations to solve the travelling-wave solutions.

Original language	English
Title of host publication	Proceedings of the International Conference on Nonlinear Mechanics, ICNM
Publisher	Shanghai Univ
Pages	620-621
Publication status	Published - 1998
Event	Proceedings of the 1998 3rd International Conference on Nonlinear Mechanics, ICNM - Shanghai, China Duration: 17 Aug 1998 → 20 Aug 1998

Conference

Conference	Proceedings of the 1998 3rd International Conference on Nonlinear Mechanics, ICNM
City	Shanghai, China
Period	17/08/98 → 20/08/98

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@inproceedings{a93b9c96a4d9402aa791a3f5e291583e,

title = "Peakons and solitary shock waves in compressible hyperelastic rods",

abstract = "The model equation (KdV equation) is used for long finite-but-small amplitude waves. However, the KdV equation does not have a solitary shock wave as its solution. A new type of equation is derived as the model equation, uτ+ζ1uuξ+σ1uξξτ = σ2(2uξuξξ+uuξξξ) (1), where ζ1, σ12 are constant coefficients related to material constants. Equation (1) is rescaled to yield ut+3uux-uxxt = γ2uxuxx+uuxxx) (2). Equation (2) is reduced to a system of ordinary differential equations to solve the travelling-wave solutions.",

author = "Dai, {Hui hui}",

year = "1998",

language = "English",

pages = "620--621",

booktitle = "Proceedings of the International Conference on Nonlinear Mechanics, ICNM",

publisher = "Shanghai Univ",

note = "Proceedings of the 1998 3rd International Conference on Nonlinear Mechanics, ICNM ; Conference date: 17-08-1998 Through 20-08-1998",

}

TY - GEN

T1 - Peakons and solitary shock waves in compressible hyperelastic rods

AU - Dai, Hui hui

PY - 1998

Y1 - 1998

N2 - The model equation (KdV equation) is used for long finite-but-small amplitude waves. However, the KdV equation does not have a solitary shock wave as its solution. A new type of equation is derived as the model equation, uτ+ζ1uuξ+σ1uξξτ = σ2(2uξuξξ+uuξξξ) (1), where ζ1, σ12 are constant coefficients related to material constants. Equation (1) is rescaled to yield ut+3uux-uxxt = γ2uxuxx+uuxxx) (2). Equation (2) is reduced to a system of ordinary differential equations to solve the travelling-wave solutions.

AB - The model equation (KdV equation) is used for long finite-but-small amplitude waves. However, the KdV equation does not have a solitary shock wave as its solution. A new type of equation is derived as the model equation, uτ+ζ1uuξ+σ1uξξτ = σ2(2uξuξξ+uuξξξ) (1), where ζ1, σ12 are constant coefficients related to material constants. Equation (1) is rescaled to yield ut+3uux-uxxt = γ2uxuxx+uuxxx) (2). Equation (2) is reduced to a system of ordinary differential equations to solve the travelling-wave solutions.

UR - http://www.scopus.com/inward/record.url?scp=0032302034&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-0032302034&origin=recordpage

M3 - RGC 32 - Refereed conference paper (with host publication)

SP - 620

EP - 621

BT - Proceedings of the International Conference on Nonlinear Mechanics, ICNM

PB - Shanghai Univ

T2 - Proceedings of the 1998 3rd International Conference on Nonlinear Mechanics, ICNM

Y2 - 17 August 1998 through 20 August 1998

ER -

Peakons and solitary shock waves in compressible hyperelastic rods

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