Exact combined traveling wave solutions and multi-symplectic structure of the variant Boussinesq-Whitham-Broer-Kaup type equations

Xiao Feng Yang, Zi Chen Deng, Qing Jun Li, Yi Wei

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

The homogeneous balance of undetermined coefficients method (HBUCM) is firstly proposed to construct not only the exact traveling wave solutions, three-wave solutions, homoclinic solutions, N-soliton solutions, but also multi-symplectic structures of some nonlinear partial differential equations (NLPDEs). By applying the proposed method to the variant Boussinesq equations (VBEs), the exact combined traveling wave solutions and a multi-symplectic structure of the VBEs are obtained directly. Then, the definition and a multi-symplectic structure of the variant Boussinesq-Whitham-Broer-Kaup type equations (VBWBKTEs) which can degenerate to the VBEs, the Whitham-Broer-Kaup equations (WBKEs) and the Broer-Kaup equations (BKEs) are given in the multi-symplectic sense. The HBUCM is also a standard and computable method, which can be generalized to obtain the exact solutions and multi-symplectic structures for some types of NLPDEs.

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume36
DOIs
StatePublished - 2016

Keywords

  • Combined traveling wave solution
  • Homogeneous balance of undetermined coefficients method
  • Multi-symplectic structure
  • Variant Boussinesq-Whitham-Broer-Kaup type equations

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