Comprehensive classification of multistability and Lyapunov exponent with multiple dynamics of nonlinear Schrödinger equation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F25%3A10256167" target="_blank" >RIV/61989100:27740/25:10256167 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s11071-024-10781-x" target="_blank" >https://link.springer.com/article/10.1007/s11071-024-10781-x</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11071-024-10781-x" target="_blank" >10.1007/s11071-024-10781-x</a>
Alternative languages
Result language
angličtina
Original language name
Comprehensive classification of multistability and Lyapunov exponent with multiple dynamics of nonlinear Schrödinger equation
Original language description
In this paper a detailed investigation of the non-linear Schr & ouml;dinger equation is presented. A comprehensive set of tools, such as chaotic attractors, Lyapunov exponents, multistability, Poincar & eacute; maps, and phase portraits are employed for the analysis of the non-perturbed and perturbed dynamical systems. In addition, the system power frequency response is analyzed, and the sensitivity to time delays is examined with return maps. To this end, the study introduces a novel classification for multi-stability and Lyapunov exponents to analyze and categorize the complex behavior of the system. The developed algorithm explores the wide parameters and initial state space, providing a complete classification of system behavior. The chaotic, quasi-periodic and periodic behaviors of the perturbed dynamical system are observed. Furthermore, the paper compares the two soliton solutions by analyzing their outcomes across a defined range of parameters to gain valuable insights into the state under which the solutions exhibit identical behavior. The classification algorithms are provided in an organized manner, and complete results are made available at the GitHub repository, ensuring that future researchers can expand upon these results. The proposed classification algorithms enable the engineers to select parameters informed by classification results. Moreover, by analyzing the results of the soliton overlap, engineers can leverage soliton co-existence behaviors to improve the resilience and performance of the system in various operating conditions. The proposed methodology has applications in optical fibers and other engineering fields.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10300 - Physical sciences
Result continuities
Project
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Continuities
O - Projekt operacniho programu
Others
Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Nonlinear Dynamics
ISSN
0924-090X
e-ISSN
1573-269X
Volume of the periodical
113
Issue of the periodical within the volume
9
Country of publishing house
US - UNITED STATES
Number of pages
30
Pages from-to
10335-10364
UT code for WoS article
001381622900001
EID of the result in the Scopus database
2-s2.0-105001079397