Abstract
Based on the Hirota’s bilinear method, a more classic limit technique is perfected to obtain second-order smooth positons. Immediately afterwards, we propose an extremely ingenious limit approach in which higher-order smooth positons and breather positons can be quickly derived from N-soliton solution. Under this ingenious technique, the smooth positons and breather positons of the modified Korteweg–de Vries system are quickly and easily derived. Compared with the generalized Darboux transformation, the approach mentioned in this paper has the following advantages and disadvantages: the advantage is that it is simple and fast and the disadvantage is that this method cannot get a concise general mathematical expression of nth-order smooth positons.
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Acknowledgements
This research is supported by the Natural Science Foundation of Guangdong Province of China (No. 2021A1515012214), the Science and Technology Program of Guangzhou (No. 2019050001), National Natural Science Foundation of China (Nos. 11775121) and K.C.Wong Magna Fund in Ningbo University. The authors would like to express their sincere thanks to Prof. Dajun Zhang for his guidance and encouragement.
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Zhang, Z., Li, B., Chen, J. et al. Construction of higher-order smooth positons and breather positons via Hirota’s bilinear method. Nonlinear Dyn 105, 2611–2618 (2021). https://doi.org/10.1007/s11071-021-06751-2
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DOI: https://doi.org/10.1007/s11071-021-06751-2