Travelling wave solutions for higher-order wave equations of KDV type (III)
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Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004
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Department of Mathematics, Honghe University, Mengzi, Yunnan 661100
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Received:
01 December 2004
Accepted:
29 June 2018
Published:
01 November 2005
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MSC :
92D30.
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By using the theory of planar dynamical systems to the travelling
wave equation of a higher order nonlinear wave equations of KdV type, the
existence of smooth solitary wave, kink wave and anti-kink wave solutions and
uncountably infinite many smooth and non-smooth periodic wave solutions are
proved. In different regions of the parametric space, the sufficient conditions to
guarantee the existence of the above solutions are given. In some conditions,
exact explicit parametric representations of these waves are obtain.
Citation: Jibin Li, Weigou Rui, Yao Long, Bin He. Travelling wave solutions for higher-order wave equations of KDV type (III)[J]. Mathematical Biosciences and Engineering, 2006, 3(1): 125-135. doi: 10.3934/mbe.2006.3.125
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Abstract
By using the theory of planar dynamical systems to the travelling
wave equation of a higher order nonlinear wave equations of KdV type, the
existence of smooth solitary wave, kink wave and anti-kink wave solutions and
uncountably infinite many smooth and non-smooth periodic wave solutions are
proved. In different regions of the parametric space, the sufficient conditions to
guarantee the existence of the above solutions are given. In some conditions,
exact explicit parametric representations of these waves are obtain.
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