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Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation

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  • Wang, Mingliang
  • Li, Xiangzheng

Abstract

We present an extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed more recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the new Hamiltonian amplitude equation introduced by Wadati et al. When the modulus m approaches to 1 and 0, then the hyperbolic function solutions (including the solitary wave solutions) and trigonometric function solutions are also given respectively. As the parameter ε goes to zero, the new Hamiltonian amplitude equation becomes the well-known nonlinear Schrödinger equation (NLS), and at least there are 37 kinds of solutions of NLS can be derived from the solutions of the new Hamiltonian amplitude equation.

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  • Wang, Mingliang & Li, Xiangzheng, 2005. "Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation," Chaos, Solitons & Fractals, Elsevier, vol. 24(5), pages 1257-1268.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:5:p:1257-1268
    DOI: 10.1016/j.chaos.2004.09.044
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    Cited by:

    1. Zeng, Xiping & Dai, Zhengde & Li, Donglong, 2009. "New periodic soliton solutions for the (3+1)-dimensional potential-YTSF equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 657-661.
    2. Sheng, Zhang, 2006. "The periodic wave solutions for the (2+1)-dimensional Konopelchenko–Dubrovsky equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1213-1220.
    3. He, Ji-Huan & Wu, Xu-Hong, 2006. "Construction of solitary solution and compacton-like solution by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 108-113.
    4. Islam, Md. Ekramul & Mannaf, Md. Abde & Khan, Kamruzzaman & Akbar, M. Ali, 2024. "Soliton’s behavior and stability analysis to a model in mathematical physics," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    5. Li, Donglong & Dai, Zhengde & Guo, Yanfeng & Zhou, Hongwei, 2009. "Doubly periodic wave solution to two-dimensional diffractive-diffusive Ginzburg–Landau equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2288-2296.
    6. Zhang, Huiqun, 2009. "A direct algebraic method applied to obtain complex solutions of some nonlinear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1020-1026.
    7. Golbabai, A. & Javidi, M., 2009. "A spectral domain decomposition approach for the generalized Burger’s–Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 385-392.
    8. Wang, Deng-Shan & Li, Hongbo, 2008. "Symbolic computation and non-travelling wave solutions of (2+1)-dimensional nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 383-390.

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