The Dynamics on Soliton Molecules and Soliton Bifurcation for an Extended Generalization of Vakhnenko Equation

Vakhnenko-type equations play a critical role in nonlinear electromagnetic and optical fiber applications. In this article, we present a new advancement in high-frequency wave propagation in electromagnetic and optical fiber applications by investigating an extended generalization of the Vakhnenko e...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems Vol. 23; no. 3
Main Authors: Ma, Yu-Lan, Li, Bang-Qing
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.07.2024
Subjects:
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Original Paper
Extended generalization of Vakhnenko equation
Bilinear method
Soliton bifurcation
Soliton molecules
Phase transition
ISSN:1575-5460, 1662-3592
Online Access:Get full text
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Summary:Vakhnenko-type equations play a critical role in nonlinear electromagnetic and optical fiber applications. In this article, we present a new advancement in high-frequency wave propagation in electromagnetic and optical fiber applications by investigating an extended generalization of the Vakhnenko equation. In our study, we employ the bilinear method and introduce an auxiliary function that combines exponential and cosine functions. By utilizing this approach, we are able to derive two distinct sets of analytical solutions for the equation. By choosing suitable parameters involved in the solutions, we identify the presence of soliton molecules and soliton bifurcation in the equation. Furthermore, for the soliton molecules, we note the existence of two distinct types of phase transitions: (i) a transition from soliton molecules to loop-like breathers, and (ii) a transition from soliton molecules to intersection solitons. Regarding soliton bifurcation, we observe phase transitions among loop-like, cusp-like, and peak-like solitons. Moreover, the results of this study illuminate that the structures of all solitons, within the context of soliton molecules and soliton bifurcation, remain stable throughout the phase transitions. This stability carries considerable significance for practical applications.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-024-01002-2