New groups of solutions to the Whitham-Broer-Kaup equation

doi:10.1007/s10483-020-2683-7

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (11): 1735-1746.doi: https://doi.org/10.1007/s10483-020-2683-7

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New groups of solutions to the Whitham-Broer-Kaup equation

Yaji WANG¹, Hang XU¹, Q. SUN²

1. State Key Lab of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, China;
2. Australian Research Council Centre of Excellence for Nanoscale BioPhotonics, School of Science, RMIT University, Melbourne, VIC 3001, Australia

Received:2020-07-28 Revised:2020-09-09 Published:2020-10-24
Contact: Q. SUN E-mail:qiang.sun@rmit.edu.au
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11872241), the Discovery Early Career Researcher Award (No. DE150100169), and the Centre of Excellence Grant funded by the Australian Research Council (No. CE140100003)

Abstract

Abstract: The Whitham-Broer-Kaup model is widely used to study the tsunami waves. The classical Whitham-Broer-Kaup equations are re-investigated in detail by the generalized projective Riccati-equation method. 20 sets of solutions are obtained of which, to the best of the authors’ knowledge, some have not been reported in literature. Bifurcation analysis of the planar dynamical systems is then used to show different phase portraits of the traveling wave solutions under various parametric conditions.

Key words: Whitham-Broer-Kaup equation, travelling wave, bifurcation analysis, projective Riccati-equation method

2010 MSC Number:

34DXX
35Q53

Yaji WANG, Hang XU, Q. SUN. New groups of solutions to the Whitham-Broer-Kaup equation. Applied Mathematics and Mechanics (English Edition), 2020, 41(11): 1735-1746.

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References

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New groups of solutions to the Whitham-Broer-Kaup equation

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