Nonlinear Dynamics

, Volume 79, Issue 2, pp 1575–1585

# Single peak solitary wave and compacton solutions of the generalized two-component Hunter–Saxton system

Original Paper

## Abstract

Dynamical system theory is applied to the generalized two-component Hunter–Saxton system. Two singular straight lines are found in the associated topological vector field. The influence of parameters as well as the singular lines on the smoothness property of the traveling wave solutions is explored in detail. We obtain the single peak solitary wave and compacton solutions for the generalized two-component Hunter–Saxton system. Asymptotic analysis and numerical simulations are provided for smooth solitary wave, peakon, cuspon and compacton solutions of the generalized two-component Hunter–Saxton system.

## Keywords

Hunter–Saxton system Solitary wave Peakon Cuspon Compacton

## Notes

### Acknowledgments

This work are supported by by the National Natural Science Foundation of China (No. 11161013 and No. 11361017), Guangxi Natural Science Foundation (No. 2014GXNSFBA118007), Foundation of Guangxi Key Lab of Trusted Software and Program for Innovative Research Team of Guilin University of Electronic Technology. The authors wish to thank the anonymous reviewers for their helpful comments and suggestions.

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## Authors and Affiliations

1. 1.School of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilinPeople’s Republic of China
2. 2.Guangxi Experiment Center of Information ScienceGuilin University of Electronic TechnologyGuilinPeople’s Republic of China