Nonlinear Optimization Of Solitons In Dispersion Management Systems

Soliton has important applications in option pricing,and provides a solution method for the nonlinear evolution equation embodied in the basic theoretical problems of economics,management,statistics,nonlinear optics and other disciplines.It is one of the research hotspots of frontiers in basic interdiscipline.Because the anti-interference capability of solitons is strengthened after passing through the dispersion management system,its signal-to-noise ratio has been significantly improved.Thus,the study of the soliton performance in the dispersion management system is of great significance.At present,as the update of nonlinear optimization technique,the transmission quality and capacity of solitons in the dispersion management system was improved.However,high nonlinearity will destroy the formation of solitons in the dispersion management system,which limits the energy output and peak power of the system.The promotion of comprehensive performance of the dispersion management system by the nonlinear optimization is a key scientific problem to be solved.On the other hand,when the signal transmission rate of the dispersion management system reaches a certain value,and solitons will be unstable.The interaction range between solitons will be greatly reduced,and the two-soliton interaction will be obvious.Therefore,the transmission effect would be affected.Compared with the two-soliton interaction,the three-soliton interaction is more complex.Due to the influence of high-order dispersion,the three-soliton interaction will produce some novel phenomena which can not be discovered in the two-soliton interaction.Besides,the nonlinear phenomena of the three-soliton interaction are more abundant,through nonlinear optimization to research the three-soliton interaction,the study of soliton array could be promoted.Therefore,it is of great significance for the dispersion management system to study the interactions of two solitons and three solitons and find effective methods to control the interaction of them.In view of the above problems,this thesis uses the bilinear method to discuss the transmission problems of the single soliton,two-soliton and three-soliton by solving the analytic solution of the third-order variable coefficient nonlinear Schrodinger(NLS)system and the fifth-order variable coefficient NLS systems(with or without the fourth-order dispersion).The nonlinear optimization of solitons in the dispersion-managed system is studied theoretically.The results are as follows:(1)The nonlinear optimization of single solitons transmission in the dispersion management system.By solving one-soliton solutions of the above three nonlinear systems,the conditions of the stable transmission of solitons are calculated,a nonlinear control method is proposed,the M-type soliton transmission is obtained,the periodic stable transmission of solitons is realized,and the transmission performance of single solitons in the dispersion management system is improved.(2)The nonlinear optimization of two-solitons transmission in the dispersion management system.By solving two-soliton solutions of the above three nonlinear systems,the periodic interaction characteristics of solitons are analyzed,the influence of each order nonlinear effect on the soliton interaction is discussed,the method of weakening the soliton interaction is proposed,and the transmission capacity of the system is increased.(3)The nonlinear optimization of three-solitons transmission in the dispersion management system.By solving three-soliton solutions of the above three nonlinear systems,the influence of high-order dispersion and nonlinear effect on the three-solitons interaction is analyzed.Through dispersion-managed and nonlinear effect,the spacing of three-solitons is effectively reduced,the interaction-free transmission of three-solitons is realized,and the transmission quality of the system is improved.By the nonlinear optimization method,this thesis improves the transmission characteristics of solitons in the dispersion management system,weakens the timing jitter of the system,reduces the influence of the twosoliton interaction and the three-soliton interaction on the system performance,enhances the comprehensive performance of the system effectively,is conducive to the theoretical research of nonlinear option price model,and provides a theoretical basis for study of interdisciplinary subjects such as mathematics,management and nonlinear optics.