Embedded solitons in the (2 + 1) -dimensional sine-Gordon equation

Wen Ye Zhong; Wei Ping Zhong; Milivoj R. Belić; Guofa Cai

doi:10.1007/s11071-020-05561-2

Embedded solitons in the (2 + 1) -dimensional sine-Gordon equation

Wen Ye Zhong, Wei Ping Zhong, Milivoj R. Belić, Guofa Cai^*

^*Corresponding author for this work

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

12 Citations (Scopus)

Abstract

An effective and simple method to solve nonlinear evolution partial differential equations is the self-similarity transformation, in which one utilizes solutions of the known equation to find solutions of the unknown. In this paper, we employ an improved similarity transformation to transform the (2 + 1) -dimensional (D) sine-Gordon (SG) equation into the (1 + 1) -D SG equation and obtain non-rational solutions of the (2 + 1) -D SG equation by utilizing the known solutions of the (1 + 1) -D SG equation. Based on the solutions obtained, and with the help of special choices of the involved solution parameters, several localized structures of the (2 + 1) -D SG model are analyzed on a finite background, such as the embedded hourglass, split silo, dumbbell, and pie solitons. Their spatiotemporal profiles are displayed, and their properties are discussed.

Original language	English
Pages (from-to)	1519-1526
Number of pages	8
Journal	Nonlinear Dynamics
Volume	100
Issue number	2
DOIs	https://doi.org/10.1007/s11071-020-05561-2
Publication status	Published - 1 Apr 2020
Externally published	Yes

Keywords

Solitons
Spatiotemporal non-rational soliton structures
The (2 + 1) -D sine-Gordon equation

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10.1007/s11071-020-05561-2

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title = "Embedded solitons in the (2 + 1) -dimensional sine-Gordon equation",

abstract = "An effective and simple method to solve nonlinear evolution partial differential equations is the self-similarity transformation, in which one utilizes solutions of the known equation to find solutions of the unknown. In this paper, we employ an improved similarity transformation to transform the (2 + 1) -dimensional (D) sine-Gordon (SG) equation into the (1 + 1) -D SG equation and obtain non-rational solutions of the (2 + 1) -D SG equation by utilizing the known solutions of the (1 + 1) -D SG equation. Based on the solutions obtained, and with the help of special choices of the involved solution parameters, several localized structures of the (2 + 1) -D SG model are analyzed on a finite background, such as the embedded hourglass, split silo, dumbbell, and pie solitons. Their spatiotemporal profiles are displayed, and their properties are discussed.",

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AU - Zhong, Wen Ye

AU - Zhong, Wei Ping

AU - Belić, Milivoj R.

AU - Cai, Guofa

PY - 2020/4/1

Y1 - 2020/4/1

N2 - An effective and simple method to solve nonlinear evolution partial differential equations is the self-similarity transformation, in which one utilizes solutions of the known equation to find solutions of the unknown. In this paper, we employ an improved similarity transformation to transform the (2 + 1) -dimensional (D) sine-Gordon (SG) equation into the (1 + 1) -D SG equation and obtain non-rational solutions of the (2 + 1) -D SG equation by utilizing the known solutions of the (1 + 1) -D SG equation. Based on the solutions obtained, and with the help of special choices of the involved solution parameters, several localized structures of the (2 + 1) -D SG model are analyzed on a finite background, such as the embedded hourglass, split silo, dumbbell, and pie solitons. Their spatiotemporal profiles are displayed, and their properties are discussed.

AB - An effective and simple method to solve nonlinear evolution partial differential equations is the self-similarity transformation, in which one utilizes solutions of the known equation to find solutions of the unknown. In this paper, we employ an improved similarity transformation to transform the (2 + 1) -dimensional (D) sine-Gordon (SG) equation into the (1 + 1) -D SG equation and obtain non-rational solutions of the (2 + 1) -D SG equation by utilizing the known solutions of the (1 + 1) -D SG equation. Based on the solutions obtained, and with the help of special choices of the involved solution parameters, several localized structures of the (2 + 1) -D SG model are analyzed on a finite background, such as the embedded hourglass, split silo, dumbbell, and pie solitons. Their spatiotemporal profiles are displayed, and their properties are discussed.

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KW - Spatiotemporal non-rational soliton structures

KW - The (2 + 1) -D sine-Gordon equation

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Embedded solitons in the (2 + 1) -dimensional sine-Gordon equation

Abstract

Keywords

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