Quasi-periodic solutions of three-component Burgers hierarchy

Wei Liu; Xianguo Geng; Bo Xue; Wei Liu; Xianguo Geng; Bo Xue

doi:10.3934/math.20231420

AIMS Mathematics

2023, Volume 8, Issue 11: 27742-27761. doi: 10.3934/math.20231420

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Research article

Quasi-periodic solutions of three-component Burgers hierarchy

1.
Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
2.
School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China

Received: 31 July 2023 Revised: 13 September 2023 Accepted: 21 September 2023 Published: 08 October 2023
MSC : 37K10, 37K20

Starting from a $ 3\times3 $ matrix spectral problem and the characteristic polynomial of the Lax matrix, we propose a trigonal curve, the associated meromorphic functions and three kinds of Abelian differentials. By discussing the asymptotic properties for the Baker-Akhiezer functions and their Riemann theta function expressions, we get quasi-periodic solutions of the three-component Burgers hierarchy. Finally, we straighten out the three-component Burgers flows.
- three-component Burgers hierarchy,
- quasi-periodic solutions,
- Baker-Akhiezer function,
- trigonal curve
Citation: Wei Liu, Xianguo Geng, Bo Xue. Quasi-periodic solutions of three-component Burgers hierarchy[J]. AIMS Mathematics, 2023, 8(11): 27742-27761. doi: 10.3934/math.20231420

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Abstract

Starting from a $ 3\times3 $ matrix spectral problem and the characteristic polynomial of the Lax matrix, we propose a trigonal curve, the associated meromorphic functions and three kinds of Abelian differentials. By discussing the asymptotic properties for the Baker-Akhiezer functions and their Riemann theta function expressions, we get quasi-periodic solutions of the three-component Burgers hierarchy. Finally, we straighten out the three-component Burgers flows.

References

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