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Application of tetragonal curves to coupled Boussinesq equations

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Abstract

The hierarchy of coupled Boussinesq equations related to a \(4\times 4\) matrix spectral problem is derived by using the zero-curvature equation and Lenard recursion equations. The characteristic polynomial of the Lax matrix is employed to introduce the associated tetragonal curve and Riemann theta functions. The detailed theory of resulting tetragonal curves is established by exploring the properties of Baker–Akhiezer functions and a class of meromorphic functions. The Abel map and Abelian differentials are used to precisely determine the linearization of various flows. Finally, algebro-geometric solutions for the entire hierarchy of coupled Boussinesq equations are obtained.

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Acknowledgements

This work is supported by National Natural Science Foundation of China (Grant Nos. 11931017, 11971441, 11971442, 12371253) and Natural Science Foundation of Henan Province (Grant No. 232300421074).

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  1. School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou, 450001, Henan, People’s Republic of China

    Xianguo Geng, Minxin Jia, Bo Xue & Yunyun Zhai

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  1. Xianguo Geng
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Geng, X., Jia, M., Xue, B. et al. Application of tetragonal curves to coupled Boussinesq equations. Lett Math Phys 114, 30 (2024). https://doi.org/10.1007/s11005-024-01780-5

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