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Dynamics of three-dimensional localized wave packets defined by the spherical Bessel function.

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Title: Dynamics of three-dimensional localized wave packets defined by the spherical Bessel function.
Authors: Dobrokhotov, S. Yu.1 (AUTHOR) s.dobrokhotov@gmail.com, Tsvetkova, A. V.1 (AUTHOR) annatsvetkova25@gmail.com
Source: Theoretical & Mathematical Physics. Mar2026, Vol. 226 Issue 3, p499-522. 24p.
Subjects: Wave packets, Bessel functions, Mathematical singularities, Asymptotic expansions, Wave equation, Symplectic manifolds
Abstract: We consider a localized wave packet which is an asymptotic solution to the three-dimensional wave equation and is generated by the spherical Bessel function at the initial time. We discuss an approach for constructing an effective representation for such a packet in terms of special functions, based on the theory of the Maslov canonical operator and the study of the dynamics of the corresponding three-dimensional Lagrangian manifold. In particular, we prove that if the initial packet has a large momentum directed along the axis, then the Bessel structure eventually vanishes and the packet spreads. Specifically, on the corresponding Lagrangian manifold, there arise singularities of the fold and cusp types, which are associated with the Airy and Pearcey functions, respectively, as well as non-generic singularities corresponding to the asymptotics in terms of the error function. [ABSTRACT FROM AUTHOR]
Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: We consider a localized wave packet which is an asymptotic solution to the three-dimensional wave equation and is generated by the spherical Bessel function at the initial time. We discuss an approach for constructing an effective representation for such a packet in terms of special functions, based on the theory of the Maslov canonical operator and the study of the dynamics of the corresponding three-dimensional Lagrangian manifold. In particular, we prove that if the initial packet has a large momentum directed along the axis, then the Bessel structure eventually vanishes and the packet spreads. Specifically, on the corresponding Lagrangian manifold, there arise singularities of the fold and cusp types, which are associated with the Airy and Pearcey functions, respectively, as well as non-generic singularities corresponding to the asymptotics in terms of the error function. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Theoretical & Mathematical Physics is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Mathematical singularities
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              Text: Mar2026
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