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Qualitative analysis and bounded traveling wave solutions for Boussinesq equation with dissipative term

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Abstract

In this paper, we study the bounded traveling wave solutions for the Boussinesq equation with dissipative term by using the theory of planar dynamical systems, and reveal the relationships between the behaviors of bounded traveling wave solutions and the dissipation coefficient. The bell profile solitary wave solution and kink profile solitary wave solution can be obtained according to the undermined coefficients method. Meanwhile, the approximate oscillatory damped solutions can be obtained. Furthermore, the global error estimation of the approximate oscillatory damped solutions is given by establishing the integral equation which reflects the relationships between approximate and exact oscillatory damped solutions.

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Acknowledgements

This paper is founded by National Natural Science Foundation of China (No. 11471215).

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  1. University of Shanghai for Science and Technology, Shanghai, China

    Yanan Hu, Weiguo Zhang & Xingqian Ling

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  1. Yanan Hu
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  2. Weiguo Zhang
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  3. Xingqian Ling
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Correspondence to Weiguo Zhang.

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Hu, Y., Zhang, W. & Ling, X. Qualitative analysis and bounded traveling wave solutions for Boussinesq equation with dissipative term. Nonlinear Dyn 105, 2595–2609 (2021). https://doi.org/10.1007/s11071-021-06750-3

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