Two-dimensional toroidal breather solutions of the self-focusing nonlinear Schrödinger equation

Zhengping Yang; Wei Ping Zhong; Milivoj R. Belić

doi:10.1016/j.physleta.2023.128715

Two-dimensional toroidal breather solutions of the self-focusing nonlinear Schrödinger equation

Zhengping Yang
, Wei Ping Zhong^*
, Milivoj R. Belić

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We introduce the ring-like toroidal breather solutions of the (2+1)-dimensional nonlinear Schrödinger (NLS) equation with Kerr nonlinearity. When the width of the toroidal pulse is much smaller than its radius, the (2+1)-dimensional NLS equation in cylindrical coordinates can be approximated by the standard (1+1)-dimensional NLS equation. Based on this NLS equation, we obtain the first-order toroidal breather solutions, and study their dynamic characteristics. In particular, we discover and present for the first time the toroidal Peregrine soliton. This research can be extended to other high-dimensional nonlinear equations and provides a practical method for the study of other high-dimensional nonlinear localized wave structures.

Original language	English
Article number	128715
Journal	Physics Letters, Section A: General, Atomic and Solid State Physics
Volume	465
DOIs	https://doi.org/10.1016/j.physleta.2023.128715
Publication status	Published - 28 Mar 2023
Externally published	Yes

Keywords

Breather
Breather excitations
Nonlinear Schrödinger equation

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10.1016/j.physleta.2023.128715

Cite this

@article{56749bc94d8d47a3ae9964d030da058a,

title = "Two-dimensional toroidal breather solutions of the self-focusing nonlinear Schr{\"o}dinger equation",

abstract = "We introduce the ring-like toroidal breather solutions of the (2+1)-dimensional nonlinear Schr{\"o}dinger (NLS) equation with Kerr nonlinearity. When the width of the toroidal pulse is much smaller than its radius, the (2+1)-dimensional NLS equation in cylindrical coordinates can be approximated by the standard (1+1)-dimensional NLS equation. Based on this NLS equation, we obtain the first-order toroidal breather solutions, and study their dynamic characteristics. In particular, we discover and present for the first time the toroidal Peregrine soliton. This research can be extended to other high-dimensional nonlinear equations and provides a practical method for the study of other high-dimensional nonlinear localized wave structures.",

keywords = "Breather, Breather excitations, Nonlinear Schr{\"o}dinger equation",

author = "Zhengping Yang and Zhong, \{Wei Ping\} and Beli{\'c}, \{Milivoj R.\}",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

year = "2023",

month = mar,

day = "28",

doi = "10.1016/j.physleta.2023.128715",

language = "English",

volume = "465",

journal = "Physics Letters, Section A: General, Atomic and Solid State Physics",

issn = "0375-9601",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Two-dimensional toroidal breather solutions of the self-focusing nonlinear Schrödinger equation

AU - Yang, Zhengping

AU - Zhong, Wei Ping

AU - Belić, Milivoj R.

PY - 2023/3/28

Y1 - 2023/3/28

N2 - We introduce the ring-like toroidal breather solutions of the (2+1)-dimensional nonlinear Schrödinger (NLS) equation with Kerr nonlinearity. When the width of the toroidal pulse is much smaller than its radius, the (2+1)-dimensional NLS equation in cylindrical coordinates can be approximated by the standard (1+1)-dimensional NLS equation. Based on this NLS equation, we obtain the first-order toroidal breather solutions, and study their dynamic characteristics. In particular, we discover and present for the first time the toroidal Peregrine soliton. This research can be extended to other high-dimensional nonlinear equations and provides a practical method for the study of other high-dimensional nonlinear localized wave structures.

AB - We introduce the ring-like toroidal breather solutions of the (2+1)-dimensional nonlinear Schrödinger (NLS) equation with Kerr nonlinearity. When the width of the toroidal pulse is much smaller than its radius, the (2+1)-dimensional NLS equation in cylindrical coordinates can be approximated by the standard (1+1)-dimensional NLS equation. Based on this NLS equation, we obtain the first-order toroidal breather solutions, and study their dynamic characteristics. In particular, we discover and present for the first time the toroidal Peregrine soliton. This research can be extended to other high-dimensional nonlinear equations and provides a practical method for the study of other high-dimensional nonlinear localized wave structures.

KW - Breather

KW - Breather excitations

KW - Nonlinear Schrödinger equation

UR - https://www.scopus.com/pages/publications/85149416105

U2 - 10.1016/j.physleta.2023.128715

DO - 10.1016/j.physleta.2023.128715

M3 - Article

AN - SCOPUS:85149416105

SN - 0375-9601

VL - 465

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

M1 - 128715

ER -

Two-dimensional toroidal breather solutions of the self-focusing nonlinear Schrödinger equation

Abstract

Keywords

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