JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (2): 77-84.doi: 10.6040/j.issn.1671-9352.0.2016.182

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Symmetry, reduction and exact solutions of the extended KP-Benjamin-Bona-Mahoney equation

LI Yu, LIU Xi-qiang*   

  1. School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, Shandong, China
  • Received:2016-04-26 Online:2017-02-20 Published:2017-01-18

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Abstract: By applying the direct symmetry method, the classical Lie symmetry and reduced equation of the extended KP-Benjamin-Bona-Mahoney equation are obtained. At the same time, through the reduced equation, a great many of solutions are derived by solving the reduction equations with(G'/G)-expansion method and the tanh function expansion method and Riccati auxiliary equation, including travelling wave solutions, the rational function solutions, hyperbolic function solutions, the trigonometric function solutions and so on. Finally, the conservation laws of the equation are obtained by using the symmetry and adjoint equations.

Key words: KP-Benjamin-Bona-Mahoney equation, reduction equation, conservation laws, exact solution, Lie point symmetry

CLC Number: 

  • O175.2
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