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Addition formulae, Bäcklund transformations, periodic solutions, and quadrilateral equations

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Abstract

Addition formulae of trigonometric and elliptic functions are used to generate Bäcklund transformations together with their connecting quadrilateral equations. As a result, we obtain the periodic solutions for a number of multidimensionally consistent affine linear and multiquadratic quadrilateral equations.

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Acknowledgements

The authors are grateful to the referees for their invaluable comments. DJZ was supported by the National Natural Science Foundation of China (Grant Nos. 11631007, 11875040), and DDZ was supported by the National Natural Science Foundation of China (Grant No. 11801289) and K. C. Wong Magna Fund in Ningbo University.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, China

    Danda Zhang

  2. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Da-jun Zhang

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  1. Danda Zhang
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  2. Da-jun Zhang
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Correspondence to Danda Zhang.

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Zhang, D., Zhang, Dj. Addition formulae, Bäcklund transformations, periodic solutions, and quadrilateral equations. Front. Math. China 14, 203–223 (2019). https://doi.org/10.1007/s11464-019-0753-0

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  • DOI: https://doi.org/10.1007/s11464-019-0753-0

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