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New Exact Jacobi Elliptic Function Solutions for the Coupled Schrödinger‐Boussinesq Equations

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  • Baojian Hong
  • Dianchen Lu

Abstract

A general algebraic method based on the generalized Jacobi elliptic functions expansion method, the improved general mapping deformation method, and the extended auxiliary function method with computerized symbolic computation is proposed to construct more new exact solutions for coupled Schrödinger‐Boussinesq equations. As a result, several families of new generalized Jacobi elliptic function wave solutions are obtained by using this method, some of them are degenerated to solitary wave solutions and trigonometric function solutions in the limited cases, which shows that the general method is more powerful than plenty of traditional methods and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.

Suggested Citation

  • Baojian Hong & Dianchen Lu, 2013. "New Exact Jacobi Elliptic Function Solutions for the Coupled Schrödinger‐Boussinesq Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:170835
    DOI: 10.1155/2013/170835
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    References listed on IDEAS

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    1. Huang, Wenhua & Liu, Yulu, 2009. "Jacobi elliptic function solutions of the Ablowitz–Ladik discrete nonlinear Schrödinger system," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 786-792.
    2. Li, Wenting & Zhang, Hongqing, 2009. "A new generalized compound Riccati equations rational expansion method to construct many new exact complexiton solutions of nonlinear evolution equations with symbolic computation," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2369-2377.
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    Cited by:

    1. Baojian Hong & Dianchen Lu & Chaudry Masood Khalique & Alvaro H. Salas & Robert A. Van Gorder, 2014. "Exact and Approximate Solutions for Nonlinear PDEs," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Wei-Xiong Chen & Ji Lin, 2014. "Some New Exact Solutions of (1+2)‐Dimensional Sine‐Gordon Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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