Multi-solitons in the model of an inhomogeneous optical fiber

Jinfang Li; Chunjiang Wang; Li Zhang; Jian Zhang; Jinfang Li; Chunjiang Wang; Li Zhang; Jian Zhang

doi:10.3934/math.20241691

AIMS Mathematics

2024, Volume 9, Issue 12: 35645-35654. doi: 10.3934/math.20241691

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Multi-solitons in the model of an inhomogeneous optical fiber

1.
School of Fundamental Education, Beijing Polytechnic College, Beijing 100042, China
2.
V.C. & V.R. Key Lab of Sichuan Province, Sichuan Normal University, Chengdu 610068, China
3.
School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 611731, China

Received: 17 October 2024 Revised: 04 December 2024 Accepted: 10 December 2024 Published: 23 December 2024
MSC : 35C08, 35Q51, 37K15

This paper was concerned with the inhomogeneous optical fiber model, which was governed by a nonlinear Schrödinger equation with variable coefficients. By spectral analysis for Lax pair of the equation, a corresponding Riemann-Hilbert problem was formulated. By solving the Riemann-Hilbert problem with simple poles, the formula of multi-soliton solutions was derived. Finally, we considered a soliton control system and obtained the one-soliton and two-soliton.
- nonlinear Schrödinger equation,
- soliton solutions,
- Riemann-Hilbert problem,
- soliton control,
- optical fibers
Citation: Jinfang Li, Chunjiang Wang, Li Zhang, Jian Zhang. Multi-solitons in the model of an inhomogeneous optical fiber[J]. AIMS Mathematics, 2024, 9(12): 35645-35654. doi: 10.3934/math.20241691

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Abstract

This paper was concerned with the inhomogeneous optical fiber model, which was governed by a nonlinear Schrödinger equation with variable coefficients. By spectral analysis for Lax pair of the equation, a corresponding Riemann-Hilbert problem was formulated. By solving the Riemann-Hilbert problem with simple poles, the formula of multi-soliton solutions was derived. Finally, we considered a soliton control system and obtained the one-soliton and two-soliton.

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