Bifurcation, Phase Portrait and Traveling Wave Solutions of the Coupled Fractional Lakshmanan–Porsezian–Daniel Equation

In this paper, we investigate the bifurcation, phase portrait and the traveling wave solutions of the coupled fractional Lakshmanan–Porsezian–Daniel equation by using the dynamical system bifurcation theory approach. Based on phase portrait, we obtain some new traveling wave solutions, which include...

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Bibliographic Details
Published in:	Qualitative theory of dynamical systems Vol. 23; no. 2
Main Authors:	Liu, Jing, Li, Zhao, He, Lin, Liu, Wei
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01.04.2024
Subjects:	Difference and Functional Equations Dynamical Systems and Ergodic Theory Mathematics Mathematics and Statistics Dynamical system bifurcation theory Traveling wave solutions Lakshmanan–Porsezian–Daniel equation
ISSN:	1575-5460, 1662-3592
Online Access:	Get full text
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Summary:	In this paper, we investigate the bifurcation, phase portrait and the traveling wave solutions of the coupled fractional Lakshmanan–Porsezian–Daniel equation by using the dynamical system bifurcation theory approach. Based on phase portrait, we obtain some new traveling wave solutions, which include Jacobi elliptic function solutions, soliton solutions, torsion wave solutions and periodic wave solutions. What’s more, we plot three-dimensional diagrams, contour plots and two-dimensional diagrams with the help of Maple, which provide a more visual demonstration of the section of this equation. The investigations are innovative and unexplored, and they can be employed to elucidate the physical phenomena that have been simulated, providing insights into their transient dynamic characteristics.
ISSN:	1575-5460 1662-3592
DOI:	10.1007/s12346-023-00935-4