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Standing Lattice Wave Patterns of a Boussinesq System

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Abstract

We prove the existence of a large family of two-dimensional standing waves that are triple periodic for a Boussinesq system which describes two-way propagation of water waves in a channel. Our proof uses the Lyapunov–Schmidt method to find the bifurcation standing waves.

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Acknowledgements

We gratefully acknowledge the reviewer for his careful reading and many insightful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

    Shenghao Li & Min Chen

  2. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH, 45221, USA

    Bingyu Zhang

Authors
  1. Shenghao Li
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  2. Min Chen
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  3. Bingyu Zhang
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Correspondence to Shenghao Li.

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Communicated by G. Iooss

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Li, S., Chen, M. & Zhang, B. Standing Lattice Wave Patterns of a Boussinesq System. J. Math. Fluid Mech. 21, 28 (2019). https://doi.org/10.1007/s00021-019-0433-6

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  • DOI: https://doi.org/10.1007/s00021-019-0433-6

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