Bifurcations of Solitary Wave Solutions to the Shallow Water Equation of Moderate Amplitude

QIN Yu-yue; DENG Zi-chen; HU Wei-peng

doi:10.3879/j.issn.1000-0887.2014.09.006

Volume 35 Issue 9

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QIN Yu-yue, DENG Zi-chen, HU Wei-peng, . Bifurcations of Solitary Wave Solutions to the Shallow Water Equation of Moderate Amplitude[J]. Applied Mathematics and Mechanics, 2014, 35(9): 1002-1010. doi: 10.3879/j.issn.1000-0887.2014.09.006

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Bifurcations of Solitary Wave Solutions to the Shallow Water Equation of Moderate Amplitude

doi: 10.3879/j.issn.1000-0887.2014.09.006

School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, Guangxi 541004, P.R.China

Funds: The National Natural Science Foundation of China(11161013；11361017)

Received Date: 2013-11-18
Rev Recd Date: 2014-06-25
Publish Date: 2014-09-15

Abstract

Abstract

The qualitative behavior and solitary wave solutions to the model equation for shallow water waves of moderate amplitude were studied with the bifurcation method for dynamic systems. The phase portraits of the system were given under different parametric conditions. The implicit expressions of the smooth solitary waves, cuspons and periodic wave solutions were obtained. Numerical simulations were conducted for the smooth solitary waves, cuspons and periodic wave solutions to the model equation. The results show that the presented findings improve the related previous conclusions.
- solitary wave,
- cuspon wave,
- periodic wave,
- bifurcation

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References(10)

References

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