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Exact Solutions and Dynamics of the Raman Soliton Model in Nanoscale Optical Waveguides, with Metamaterials, Having Polynomial Law Nonlinearity

Wu Wen-Tsun Key Laboratory, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, P. R. China

School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China

E-mail Address: zy4233@hqu.edu.cn

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and

Jibin Li

School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, P. R. China

Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China

E-mail Address: lijb@zjnu.cn

E-mail Address: lijb@hqu.edu.cn

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https://doi.org/10.1142/S0218127417501887Cited by:3 (Source: Crossref)

Abstract

Raman soliton model in nanoscale optical waveguides, with metamaterials, having polynomial law nonlinearity is investigated by the method of dynamical systems. The functions $ϕ (ξ)$ in the solutions $q (x, t) = ϕ (ξ) exp (i (- k x + ω t)),$ $(ξ = x - v t)$ satisfy a singular planar dynamical system having two singular straight lines. By using the bifurcation theory method of dynamical systems to the equations of $ϕ (ξ)$ , under 23 different parameter conditions, bifurcations of phase portraits and exact periodic solutions, homoclinic and heteroclinic solutions, periodic peakons and peakons as well as compacton solutions for this planar dynamical system are obtained. 92 exact explicit solutions of system (6) are derived.

Keywords:

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