Qualitative Theory of Dynamical Systems

, Volume 18, Issue 3, pp 741–760 | Cite as

Dynamical Behavior of Traveling Wave Solutions of a Long Waves–Short Waves Resonance Model

  • Temesgen Desta LetaEmail author
  • Jibin Li


In this paper, we consider the model of a long waves–short waves, which model the resonant interaction between the ocean wave, to investigate the qualitative behavior of traveling wave solutions of dynamical systems. To understand the underlying complex dynamics, we apply the bifurcation method, that serve as a mechanism for fascinating the physical behavior such as solitons and we obtain all possible phase portraits of the system under various conditions depending on the parameters associated with the planar dynamical system.


Traveling wave solution Bifurcation Hamiltonian system Long wave-short wave model 

Mathematics Subject Classification

34C23 34C37 37D45 



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Authors and Affiliations

  1. 1.Department of MathematicsDilla UniversityDillaEthiopia
  2. 2.Department of MathematicsZhejiang Normal UniversityJinhuaPeople’s Republic of China
  3. 3.School of Mathematical SciencesHuaqiao UniversityQuanzhouPeople’s Republic of China

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