Nonlinear control for soliton interactions in optical fiber systems
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ORIGINAL PAPER
Nonlinear control for soliton interactions in optical fiber systems Pei Zhang · Cheng Hu · Qin Zhou Anjan Biswas · Wenjun Liu
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Received: 22 June 2020 / Accepted: 29 July 2020 © Springer Nature B.V. 2020
Abstract The realization of soliton control and soliton quality balance is one of the key research contents of optical communications. In order to better reflect the nonlinear interactions during soliton transmission and investigate their change rule, it is necessary to use the transmission model based on nonlinear interaction of solitons to study their characteristics. In this paper, we consider the fifth-order nonlinear Schrödinger equation with variable dispersion and nonlinear effects to realize soliton control and improve soliton quality. Analytic solutions of this equation are presented by the bilinear method, and the transmission and interaction characteristics of solitons in real P. Zhang · C. Hu · W. Liu · State Key Laboratory of Information Photonics and Optical Communications, School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China e-mail: [email protected] Q. Zhou (B) School of Electronics and Information Engineering, Wuhan Donghu University, Wuhan 430212, China e-mail: [email protected] A. Biswas Department of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL 35762-4900, USA A. Biswas Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia A. Biswas Department of Applied Mathematics, National Research Nuclear University, 31 Kashirskoe Shosse, Moscow, Russian Federation 115409
fiber systems are studied. Influences of dispersion and nonlinear effects on them are analyzed. The nonlinear control based on the linear optical fiber is realized by studying the interactions between two adjacent solitons. Keywords Solitons · Nonlinear control · Nonlinear Schrödinger equations · Analytic solution
1 Introduction Nonlinear science is the core of modern science, and some phenomena in natural science, such as soliton, fractal and chaos are all assumed to be nonlinear problems [1–4]. Nonlinearity can produce new phenomena essentially, which are impossibly caused by perturbation theory based on linear model approach [5– 8]. Therefore, using the nonlinear model to study the physical phenomenon is being the certainty of modern science development. In fact, some descriptions of nonlinear phenomena involve nonlinear evolution equations (NLEEs) [9–19]. In recent years, with the deepening of research on nonlinear theory, a variety of new approaches for solving NLEEs are proposed like the bilinear method, homogeneous balance method and so on [20–23]. Meanwhile, researchers can also obtain numerous localized excitations from different nonlinear systems. Finding analytic solutions of NLEEs and studying their localized excitations have always been
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an important issue in the research area of nonlinear theoreticians [24–27]. Among NLEEs, nonlinear Schrödinger equation (NLSE) is a fundamental equation in
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