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Auto-Bäcklund Transformation, Similarity Reductions and Solitons of an Extended (\(2+1\))-Dimensional Coupled Burgers System in Fluid Mechanics

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Abstract

Burgers-type equations are seen in cosmology, hydrodynamics, plasma physics, hurricane dynamics, statistical dynamics, traffic modelling, etc. For an extended (\(2+1\))-dimensional coupled Burgers system in fluid mechanics, concerning the velocity components in the fluid-related problems, our symbolic computation brings forth an auto-Bäcklund transformation with some solitons, and two sets of the similarity reductions. Our results rely on the coefficients in the system.

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Data availibility statement

Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

Notes

  1. Other types of the nonlinear models could be seen [17,18,19,20,21,22,23,24,25,26,27,28, 28, 29].

  2. More fluid-mechanics discussions have been presented [46,47,48,49,50,51,52,53,54,55,56,57,58,59,60].

  3. We make clear that the similarity reduction in Ref. [6] is different from the ones in this paper, while different models than System (4) in this paper have been studied elsewhere [3,4,5, 76].

  4. Other types of the auto-Bäcklund transformations could be seen, e.g., the bilinear auto-Bäcklund transformations [77,78,79,80,81,82,83,84]

  5. which is different from that in Ref. [6]

  6. similar to those in Refs. [85,86,87,88,89]

  7. details ignored

  8. By the way, the one reported in Ref. [6] is steady. Presently-interesting symbolic-computation contributions can be seen in Refs. [63, 74, 92, 93].

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Acknowledgements

We express our sincere thanks to the Editors and Reviewers for their valuable comments. This work has been supported by the National Natural Science Foundation of China under Grant No. 11871116 and the Fundamental Research Funds for the Central Universities of China under Grant No. 2019XD-A11. XYG also thanks the National Scholarship for Doctoral Students of China.

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  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Xin-Yi Gao, Yong-Jiang Guo & Wen-Rui Shan

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  1. Xin-Yi Gao
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  2. Yong-Jiang Guo
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  3. Wen-Rui Shan
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Correspondence to Xin-Yi Gao, Yong-Jiang Guo or Wen-Rui Shan.

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Gao, XY., Guo, YJ. & Shan, WR. Auto-Bäcklund Transformation, Similarity Reductions and Solitons of an Extended (\(2+1\))-Dimensional Coupled Burgers System in Fluid Mechanics. Qual. Theory Dyn. Syst. 21, 60 (2022). https://doi.org/10.1007/s12346-022-00574-1

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