Advances in Difference Equations | |
Riemann–Hilbert approach and N-soliton solution for an eighth-order nonlinear Schrödinger equation in an optical fiber | |
Tie-Cheng Xia1  Zhou-Zheng Kang2  Wen-Xiu Ma3  | |
[1] 0000 0001 2323 5732, grid.39436.3b, Department of Mathematics, Shanghai University, Shanghai, China;0000 0001 2323 5732, grid.39436.3b, Department of Mathematics, Shanghai University, Shanghai, China;0000 0000 8547 6673, grid.411647.1, College of Mathematics, Inner Mongolia University for Nationalities, Tongliao, China;0000 0001 2353 285X, grid.170693.a, Department of Mathematics and Statistics, University of South Florida, Tampa, USA;0000 0001 2219 2654, grid.453534.0, Department of Mathematics, Zhejiang Normal University, Jinhua, China; | |
关键词: Eighth-order nonlinear Schrödinger equation; Riemann–Hilbert approach; Soliton solutions; 35C08; | |
DOI : 10.1186/s13662-019-2121-5 | |
来源: publisher | |
【 摘 要 】
This paper aims to present an application of the Riemann–Hilbert approach to treat higher-order nonlinear differential equation that is an eighth-order nonlinear Schrödinger equation arising in an optical fiber. Starting from the spectral analysis of the Lax pair, a matrix Riemann–Hilbert problem is formulated strictly. Then, by solving the obtained Riemann–Hilbert problem under the reflectionless case, N-soliton solution is generated for the eighth-order nonlinear Schrödinger equation. Finally, the localized structures and dynamic behaviors of one- and two-soliton solutions are illustrated by some figures.
【 授权许可】
CC BY
【 预 览 】
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