Method for solving systems of differential equations with application in nonlinear optics

作     者：Aneliya Dakova Diana Dakova Zara Kasapeteva Anjan Biswas Valeri Slavchev Lubomir Kovachev 

作者机构：1Physics and Technology Faculty University of Plovdiv ”Paisii Hilendarski” 24 Tsar Asen Str. 4000 Plovdiv Bulgaria 2Institute of Electronics Bulgarian Academy of Sciences 72 Tzarigradcko shossee 1784 Sofia Bulgaria 3Faculty of Mechanical Engineering Technical University of Sofia - Branch Plovdiv 25 Tsanko Diustabanov St 4000 Plovdiv Bulgaria 4Department of Applied Mathematics National Research Nuclear University 31 Kashirskoe Hwy Moscow–115409 Russian Federation 5Mathematical Modeling and Applied Computation (MMAC) Research Group Department of Mathematics King Abdulaziz University Jeddah–21589 Saudi Arabia 6Department of Mathematics and Applied Mathematics Sefako Makgatho Health Sciences University Medunsa– 0204 Pretoria South Africa 7Department of Physics Chemistry and Mathematics Alabama A&M University Normal AL 35762–4900 USA 8Faculty of Pharmacy Medical University - Plovdiv 15 Vasil Aprilov Bul. 4002 Plovdiv Bulgaria 

出 版 物：《AIP Conference Proceedings》 

年 卷 期：2022年第2505卷第1期

学科分类：07[理学] 0702[理学-物理学] 

摘      要：The present paper focuses on a specific method for solving systems of differential equations with application in nonlinear optics. The basic system is presented by two coupled nonlinear differential equations, written in dimensionless form, which govern the propagation of light pulses in optical fibers. The mathematical algorithm is described in detail in the article. The system is analytically solved. The obtained solutions of the equations are in the form of special functions - Jacobi elliptic delta function. They determine the periodical energy exchange between light pulses. The mathematical method can be applied for pulses with arbitrary initial intensities, generalized phase and wave number mismatch.