JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (10): 51-60.doi: 10.6040/j.issn.1671-9352.0.2017.607

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Differential invariants and exact solutions of variable coefficients Benjamin-Bona-Mahony-Burgers equation

LI Hui-hui, LIU Xi-qiang*, XIN Xiang-peng   

  1. School of Mathematical Science, Liaocheng University, Liaocheng 252059, Shandong, China
  • Received:2017-11-24 Online:2018-10-20 Published:2018-10-09

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Abstract: The Lie symmetry method is performed for the variable coefficients Benjamin-Bona-Mahony-Burgers(BBMB)equation and the continuous equivalence transformations are obtained. Starting with the equivalent algebra, the differential invariants of order one are constructed. It is found that there is no zero-order differential invariant for this equation, but there are eight first-order invariants that are independent of each other. Using the obtained first-order differential invariants, we make the group classification. Finally, the general variable coefficient BBMB equations are mapped to the constant coefficient BBM equation or Burgers equation or BBMB equation by the given equivalent transformation. And then a series of new exact solutions of those variable coefficient equations are obtained. The images of the exact solution of the special BBM equation with variable coefficients and Burgers equation of the exact solution are made.

Key words: classical Lie group method, nonlinear evolution equations, group classification, variable coefficients BBMB equation, differential invariants

CLC Number: 

  • O175.2
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