The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations ...The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.展开更多
Optical solitons,as self-sustaining waveforms in a nonlinear medium where dispersion and nonlinear effects are balanced,have key applications in ultrafast laser systems and optical communications.Physics-informed neur...Optical solitons,as self-sustaining waveforms in a nonlinear medium where dispersion and nonlinear effects are balanced,have key applications in ultrafast laser systems and optical communications.Physics-informed neural networks(PINN)provide a new way to solve the nonlinear Schrodinger equation describing the soliton evolution by fusing data-driven and physical constraints.However,the grid point sampling strategy of traditional PINN suffers from high computational complexity and unstable gradient flow,which makes it difficult to capture the physical details efficiently.In this paper,we propose a residual-based adaptive multi-distribution(RAMD)sampling method to optimize the PINN training process by dynamically constructing a multi-modal loss distribution.With a 50%reduction in the number of grid points,RAMD significantly reduces the relative error of PINN and,in particular,optimizes the solution error of the(2+1)Ginzburg–Landau equation from 4.55%to 1.98%.RAMD breaks through the lack of physical constraints in the purely data-driven model by the innovative combination of multi-modal distribution modeling and autonomous sampling control for the design of all-optical communication devices.RAMD provides a high-precision numerical simulation tool for the design of all-optical communication devices,optimization of nonlinear laser devices,and other studies.展开更多
Optical solitons in mode-locked fiber lasers and optical communication links have various applications. Thestudy of transmission modes of optical solitons necessitates the investigation of the relationship between the...Optical solitons in mode-locked fiber lasers and optical communication links have various applications. Thestudy of transmission modes of optical solitons necessitates the investigation of the relationship between theequation parameters and soliton evolution employing deep learning techniques. However, the existing identificationmodels exhibit a limited parameter domain search range and are significantly influenced by initialization.Consequently, they often result in divergence toward incorrect parameter values. This study harnessed reinforcementlearning to revamp the iterative process of the parameter identification model. By developing a two-stageoptimization strategy, the model could conduct an accurate parameter search across arbitrary domains. Theinvestigation involved several experiments on various standard and higher-order equations, illustrating that theinnovative model overcame the impact of initialization on the parameter search, and the identified parametersare guided toward their correct values. The enhanced model markedly improves the experimental efficiency andholds significant promise for advancing the research of soliton propagation dynamics and addressing intricatescenarios.展开更多
基金supported by the National Key R&D Program of China(Grant No.2022YFA1604200)the National Natural Science Foundation of China(Grant No.12261131495)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21).
文摘The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1604200)National Natural Science Foundation of China(Grant No.12261131495)+1 种基金Beijing Municipal Science and Technology Commission,Adminitrative Commission of Zhongguancun Science Park(Grant No.Z231100006623006)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21)。
文摘Optical solitons,as self-sustaining waveforms in a nonlinear medium where dispersion and nonlinear effects are balanced,have key applications in ultrafast laser systems and optical communications.Physics-informed neural networks(PINN)provide a new way to solve the nonlinear Schrodinger equation describing the soliton evolution by fusing data-driven and physical constraints.However,the grid point sampling strategy of traditional PINN suffers from high computational complexity and unstable gradient flow,which makes it difficult to capture the physical details efficiently.In this paper,we propose a residual-based adaptive multi-distribution(RAMD)sampling method to optimize the PINN training process by dynamically constructing a multi-modal loss distribution.With a 50%reduction in the number of grid points,RAMD significantly reduces the relative error of PINN and,in particular,optimizes the solution error of the(2+1)Ginzburg–Landau equation from 4.55%to 1.98%.RAMD breaks through the lack of physical constraints in the purely data-driven model by the innovative combination of multi-modal distribution modeling and autonomous sampling control for the design of all-optical communication devices.RAMD provides a high-precision numerical simulation tool for the design of all-optical communication devices,optimization of nonlinear laser devices,and other studies.
基金National Key Research and Development Program of China(Grant No.2022YFA1604200)Beijing Municipal Science and Technology Commission,Administrative Commission of Zhongguancun Science Park(Grant No.Z231100006623006).
文摘Optical solitons in mode-locked fiber lasers and optical communication links have various applications. Thestudy of transmission modes of optical solitons necessitates the investigation of the relationship between theequation parameters and soliton evolution employing deep learning techniques. However, the existing identificationmodels exhibit a limited parameter domain search range and are significantly influenced by initialization.Consequently, they often result in divergence toward incorrect parameter values. This study harnessed reinforcementlearning to revamp the iterative process of the parameter identification model. By developing a two-stageoptimization strategy, the model could conduct an accurate parameter search across arbitrary domains. Theinvestigation involved several experiments on various standard and higher-order equations, illustrating that theinnovative model overcame the impact of initialization on the parameter search, and the identified parametersare guided toward their correct values. The enhanced model markedly improves the experimental efficiency andholds significant promise for advancing the research of soliton propagation dynamics and addressing intricatescenarios.
