Riemann–Hilbert approach and N-soliton solution for an eighth-order nonlinear Schrödinger equation in an optical fiber

Advances in Difference Equations

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