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Residual symmetry analysis and CRE integrability of the (3 + 1) -dimensional Burgers system

  • Xi-Zhong LiuEmail author
  • Jun Yu
  • Zhi-Mei Lou
  • Xian-Min Qian
Regular Article

Abstract.

The residual symmetry of the (3 + 1) -dimensional Burgers system is localized to a Lie point symmetry in a prolonged system and the corresponding finite transformation is obtained by using Lie’s first theorem. By further localize the linear superposition of multiple residual symmetries, the N -th Bäcklund transformations (BT) of the (3 + 1) -dimensional Burgers system are also got. By applying the standard Lie symmetry method to the prolonged system, not only the Lie symmetry group but also the symmetry reduction solutions are obtained, which include abundant interaction solutions between solitons and nonlinear waves. Furthermore, the (3 + 1) -dimensional Burgers system is proved to have consistent Riccati expansion (CRE) property, based on which some new BTs are given.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Xi-Zhong Liu
    • 1
    Email author
  • Jun Yu
    • 1
  • Zhi-Mei Lou
    • 1
  • Xian-Min Qian
    • 2
  1. 1.Institute of Nonlinear ScienceShaoxing UniversityShaoxingChina
  2. 2.Yuanpei CollegeShaoxing UniversityShaoxingChina

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