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Bifurcations and Exact Solutions of the RamanSoliton Model in Nanoscale Optical Waveguideswith Metamaterials
  
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KeyWord:Raman soliton model; Planar dynamical system; Bifurcations of phase portraits; Traveling wave solutions
Author NameAffiliation
Yan Zhou School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China 
Jinsen Zhuang School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China 
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Abstract:
      In this paper, we study Raman soliton model in nanoscale optical waveguides with metamaterials, having polynomial law non-linearity. By using the bifurcation theory method of dynamical systems to the equations of $\phi(\xi)$, under 24 different parameter conditions, we obtain bifurcations of phase portraits and different traveling wave solutions including periodic solutions, homoclinic and heteroclinic solutions for planar dynamical system of the Raman soliton model. Under different parameter conditions, 24 exact explicit parametric representations of the traveling wave solutions are derived. The dynamic behavior of these traveling wave solutions are meaningful and helpful for us to understand the physical structures of the model.