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Exact traveling wave solutions and \(L^{1}\) stability for the shallow water wave model of moderate amplitude

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Abstract

In this paper, we developed, for the first time, the exact expressions of several periodic travelling wave solutions and a solitary wave solution for a shallow water wave model of moderate amplitude. Then, we present the existence theorem of the global weak solutions. Finally, we prove the stability of solution in \(L^{1}(R)\) space for the Cauchy problem of the equation.

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Acknowledgments

This work was partly supported by the National Natural Science Foundation of China [grant number 11471263]; Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing [grant number 2013QZJ02], [grant number 2014QYJ03]; Scientific Research Foundation of the Education Department of Sichuan province Project [grant number 16ZA0265]; SUSER [grant number 2014RC03]. The authors are indebted to the referee for giving some important suggestions, which improved the presentations of this paper.

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  1. College of Science, Sichuan University of Science and Engineering, Zigong, 643000, China

    Ying Wang & Yunxi Guo

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  1. Ying Wang
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  2. Yunxi Guo
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Correspondence to Ying Wang.

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Wang, Y., Guo, Y. Exact traveling wave solutions and \(L^{1}\) stability for the shallow water wave model of moderate amplitude. Anal.Math.Phys. 7, 245–254 (2017). https://doi.org/10.1007/s13324-016-0139-3

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  • DOI: https://doi.org/10.1007/s13324-016-0139-3

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