Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (3): 753-764.doi: 10.1016/S0252-9602(16)30037-6

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INVARIANT SUBSPACES AND GENERALIZED FUNCTIONAL SEPARABLE SOLUTIONS TO THE TWO-COMPONENT b-FAMILY SYSTEM

Lu YAN1, Zhenhua SHI2, Hao WANG2, Jing KANG3   

  1. 1. Xingzhi College, Xi'an University of Finance and Economics, Xi'an 710038, China;
    2. School of Mathematics, Northwest University, Xi'an 710069, China;
    3. Center for Nonlinear Studies and School of Mathematics, Northwest University, Xi'an 710069, China
  • Received:2015-03-31 Revised:2015-11-24 Online:2016-06-25 Published:2016-06-25
  • Contact: Jing KANG,E-mail:jingkang@nwu.edu.cn E-mail:jingkang@nwu.edu.cn
  • Supported by:

    This work is supported by NSFC (11471260) and the Foundation of Shannxi Education Committee (12JK0850).

Abstract:

Invariant subspace method is exploited to obtain exact solutions of the two-component b-family system. It is shown that the two-component b-family system admits the generalized functional separable solutions. Furthermore, blow up and behavior of those exact solutions are also investigated.

Key words: invariant subspace, generalized conditional symmetry, generalized functional separable solution, Camassa-Holm equation, two-component b-family system

CLC Number: 

  • 37K05
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