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Solitary and Periodic Wave Solutions of Sasa–Satsuma Equation and Their Relationship with Hamilton Energy

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  • Weiguo Zhang
  • Xingqian Ling
  • Bei-Bei Wang
  • Shaowei Li

Abstract

In this paper, we study the exact solitary wave solutions and periodic wave solutions of the S-S equation and give the relationships between solutions and the Hamilton energy of their amplitudes. First, on the basis of the theory of dynamical system, we make qualitative analysis on the amplitudes of solutions. Then, by using undetermined hypothesis method, the first integral method, and the appropriate transformation, two bell-shaped solitary wave solutions and six exact periodic wave solutions are obtained. Furthermore, we discuss the evolutionary relationships between these solutions and find that the appearance of these solutions for the S-S equation is essentially determined by the value which the Hamilton energy takes. Finally, we give some diagrams which show the changing process from the periodic wave solutions to the solitary wave solutions when the Hamilton energy changes.

Suggested Citation

  • Weiguo Zhang & Xingqian Ling & Bei-Bei Wang & Shaowei Li, 2020. "Solitary and Periodic Wave Solutions of Sasa–Satsuma Equation and Their Relationship with Hamilton Energy," Complexity, Hindawi, vol. 2020, pages 1-17, April.
    • Handle: RePEc:hin:complx:8760179
    DOI: 10.1155/2020/8760179
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    Cited by:

    1. Sugati, Taghreed G. & Seadawy, Aly R. & Alharbey, R.A. & Albarakati, W., 2022. "Nonlinear physical complex hirota dynamical system: Construction of chirp free optical dromions and numerical wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    2. Simbawa, Eman & Seadawy, Aly R. & Sugati, Taghreed G., 2021. "Dispersive wave propagation of the nonlinear Sasa-Satsuma dynamical system with computational and analytical soliton solutions," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).

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