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Bifurcations and nonlinear wave solutions for the generalized two-component integrable Dullin–Gottwald–Holm system

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Abstract

In this paper, we study the bifurcations and nonlinear wave solutions for a generalized two-component integrable Dullin–Gottwald–Holm system. Through the bifurcations of phase portraits, we not only show the existence of several types of nonlinear wave solutions, including solitary waves, peakons, periodic cusp waves, periodic waves, compacton-like waves and kink-like waves, but also obtain their implicit expressions. Additionally, the numerical simulations of the nonlinear wave solutions are given to show the correctness of our results.

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Acknowledgments

This research is supported by the National Natural Science Foundation of Fujian Province (No. 2015J05008), Science and Technology Program (Class A) of the Education Department of Fujian Province (No. JA14023) and the foundation of Huaqiao University (No. 12BS223).

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  1. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, People’s Republic of China

    Zhenshu Wen

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  1. Zhenshu Wen
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Wen, Z. Bifurcations and nonlinear wave solutions for the generalized two-component integrable Dullin–Gottwald–Holm system. Nonlinear Dyn 82, 767–781 (2015). https://doi.org/10.1007/s11071-015-2195-x

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  • DOI: https://doi.org/10.1007/s11071-015-2195-x

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