Bifurcations and Exact Solutions of the Raman Soliton Model in Nanoscale Optical Waveguides with Metamaterials
Year: 2021
Author: Yan Zhou, Jinsen Zhuang
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 1 : pp. 145–165
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 behaviors of these traveling wave solutions are meaningful and helpful for us to understand the physical structures of the model.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2021.145
Journal of Nonlinear Modeling and Analysis, Vol. 3 (2021), Iss. 1 : pp. 145–165
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 21
Keywords: Raman soliton model Planar dynamic systems Bifurcations of phase portraits Traveling wave solutions.