https://doi.org/10.1140/epjp/s13360-024-05402-w
Regular Article
Shannon entropy and fisher information of solitons for the cubic nonlinear Schrödinger equation
Faculty of Science, Kanagawa University, 3-27-1 Rokkakubashi, 221-8686, Yokohama, Kanagawa, Japan
Received:
3
June
2024
Accepted:
25
June
2024
Published online:
8
July
2024
We treat an issue of information encoded in the profiles of solitary waves. The solitary waves as the solutions of nonlinear equations contain information in their own right. So far, however, the analyses of intrinsic information of soliton profiles have not been focused and are lacking. In this study, we use information contents in information theory; that is, we calculate Shannon entropy and Fisher information of solution intensities of the cubic nonlinear Schrödinger equation (NLSE), a well-known prototypical model of solitons. The significant reason for using this model is that some analytical soliton forms are available. Our key findings include that Shannon entropy of the bright soliton that appears in the self-focusing case, either increases or decreases depending on the nonlinear coefficient as a function of the dispersion coefficient, while Fisher information monotonically decreases. Our numerical findings also reveal that these information measures associated with the soliton solutions such as Peregrine waves, Akhmediev breathers, and Kuznetzov-Ma solitons exhibit multi-modal structures corresponding to each soliton profile. Specifically, the temporal patterns for Peregrine solitons and Akhmediev breathers show periodic peaks whose heights and intervals depend on the control parameter. This study concludes that the information contents serve as an important characteristics of the structure of solitary waves, providing a novel perspective on the properties of the soliton profiles associated with NLSEs.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
