Dynamical Behavior of Traveling Wave Solutions of a Long Waves–Short Waves Resonance Model
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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.
KeywordsTraveling wave solution Bifurcation Hamiltonian system Long wave-short wave model
Mathematics Subject Classification34C23 34C37 37D45
- 13.Li, J.: Singular Nonlinear Traveling Wave Equations: Bifurcations and Exact Solution. Mathematics Monograph Series, pp. 24–48. Science Press, Beijing (2013)Google Scholar