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Generalized involutive symmetry and its application in integrability of differential systems

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Abstract

In this paper, we study the generalized involution and its properties together with those of generalized reversible differential systems induced by the generalized involution. As an application of our theory we discuss integrability of the generalized reversible differential systems and their related integrability varieties. We propose also a computational approach to find subfamilies of partially integrable systems inside some families of polynomial differential systems.

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Acknowledgements

The first and third authors are supported by innovation program of Shanghai Municipal Education Commission grant 15ZZ012. The second author is supported by the Slovenian Research Agency. The third author is partially supported by NNSF of China grants 11271252 and 11671254. The three authors are also supported by a Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme, FP7-PEOPLE-2012-IRSES-316338.

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Lijun Wei

  2. Center for Applied Mathematics and Theoretical Physics Faculty of Natural Science and Mathematics, University of Maribor, 2000, Maribor, Slovenia

    Valery Romanovski

  3. School of Mathematical Sciences, and MOE–LSC, Shanghai Jiao Tong University, Shanghai, 200240, People’s Republic of China

    Xiang Zhang

Authors
  1. Lijun Wei
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  2. Valery Romanovski
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  3. Xiang Zhang
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Correspondence to Xiang Zhang.

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Wei, L., Romanovski, V. & Zhang, X. Generalized involutive symmetry and its application in integrability of differential systems. Z. Angew. Math. Phys. 68, 132 (2017). https://doi.org/10.1007/s00033-017-0880-y

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  • DOI: https://doi.org/10.1007/s00033-017-0880-y

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