Abstract
The stretch-twist-fold (STF) flow, as a special case of Stokes flows, arises naturally in dynamo theory. The paper studies the integrability of the STF flow. The paper provides a complete classification of the irreducible Darboux polynomials for the system with all values of the parameter alpha. When the parameter is zero, the STF flow is integrable. When the parameter is more than zero, it is proved not to be Darboux integrable. The paper also proves the system has neither exponential factors nor polynomial first integrals at the parameter alpha more than zero.
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Acknowledgements
We express our sincere thanks to the anonymous referees for their rigorous comments and valuable suggestions helping to improve the original manuscript. The research is supported by the National Natural Science Foundation of China (No. 11271139), the Science and Technology Planning Project of Guangdong Province, China (No. 2012B061800088), and the Fundamental Research Funds for the Central Universities (No. 2013ZM0115).
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Bao, J., Yang, Q. Darboux integrability of the stretch-twist-fold flow. Nonlinear Dyn 76, 797–807 (2014). https://doi.org/10.1007/s11071-013-1170-7
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DOI: https://doi.org/10.1007/s11071-013-1170-7