In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models ar...In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models are turned into multi-component real models by proper transformations. Lie symmetries are obtained via the classical Lie group method, and the results for the coupled complex short pulse equations contain the existing results as particular cases.Based on the linearizing operator and adjoint linearizing operator for the two real systems,adjoint symmetries can be obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair(SA) method. Relationships between the nonlinear selfadjointness method and the SA method are investigated.展开更多
In this work, new plain and composite high-energy solitons of the cubic–quintic Swift–Hohenberg equation were numerically found. Starting from a composite pulse found by Soto-Crespo and Akhmediev and changing some p...In this work, new plain and composite high-energy solitons of the cubic–quintic Swift–Hohenberg equation were numerically found. Starting from a composite pulse found by Soto-Crespo and Akhmediev and changing some parameter values allowed us to find these high energy pulses. We also found the region in the parameter space in which these solutions exist. Some pulse characteristics, namely, temporal and spectral profiles and chirp, are presented. The study of the pulse energy shows its independence of the dispersion parameter but its dependence on the nonlinear gain. An extreme amplitude pulse has also been found.展开更多
Four novel mononuclear ruthenium(II) complexes [Ru-(dmb) 2L] 2+ [dmb=4,4′-dimethyl-2,2′-bipyridine, L=imid-azo-[4,5-f]phenanthroline (IP), 2-phenylimidazo-phenanthroline (PIP), 2-(4′-hydroxyphenyl)imidazo-phe...Four novel mononuclear ruthenium(II) complexes [Ru-(dmb) 2L] 2+ [dmb=4,4′-dimethyl-2,2′-bipyridine, L=imid-azo-[4,5-f]phenanthroline (IP), 2-phenylimidazo-phenanthroline (PIP), 2-(4′-hydroxyphenyl)imidazo-phenanthroline (HOP), 2-(4′-dimethylami- nophenyl)imidazo-phenanthroline (DMNP)] were synthesized and characterized by ES-MS, 1H NMR, UV-vis and electrochemistry. The nonlinear optical properties of the ruthenium(II) complexes were investigated by Z-scan techniques with 12 ns laser pulse at 540 nm, and all of them exhibit both nonlinear optical (NLO) absorption and self-defocusing effect. The corresponding effective NLO susceptibility |χ 3| of the complexes is in the range of 2.68×10 -12-4.57×10 -12 esu.展开更多
基金funded by the National Natural Science Foundation of China(No.12105073)Science and Technology Program of Colleges and Universities in Hebei Province(No.QN2020144)+2 种基金Science and Technology Plan Project(Special Program for Soft Science)in Hebei Province(No.20556201D)Scientific Research and Development Program Fund Project of Hebei University of Economics and Business(Nos.2020YB15,2020YB12 and 2021ZD07)Youth Team Support Program of Hebei University of Economics and Business。
文摘In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models are turned into multi-component real models by proper transformations. Lie symmetries are obtained via the classical Lie group method, and the results for the coupled complex short pulse equations contain the existing results as particular cases.Based on the linearizing operator and adjoint linearizing operator for the two real systems,adjoint symmetries can be obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair(SA) method. Relationships between the nonlinear selfadjointness method and the SA method are investigated.
基金FCT(Fundacao para a Ciência e Tecnologia)for supporting this work through the Project UID/CTM/50025/2013
文摘In this work, new plain and composite high-energy solitons of the cubic–quintic Swift–Hohenberg equation were numerically found. Starting from a composite pulse found by Soto-Crespo and Akhmediev and changing some parameter values allowed us to find these high energy pulses. We also found the region in the parameter space in which these solutions exist. Some pulse characteristics, namely, temporal and spectral profiles and chirp, are presented. The study of the pulse energy shows its independence of the dispersion parameter but its dependence on the nonlinear gain. An extreme amplitude pulse has also been found.
文摘Four novel mononuclear ruthenium(II) complexes [Ru-(dmb) 2L] 2+ [dmb=4,4′-dimethyl-2,2′-bipyridine, L=imid-azo-[4,5-f]phenanthroline (IP), 2-phenylimidazo-phenanthroline (PIP), 2-(4′-hydroxyphenyl)imidazo-phenanthroline (HOP), 2-(4′-dimethylami- nophenyl)imidazo-phenanthroline (DMNP)] were synthesized and characterized by ES-MS, 1H NMR, UV-vis and electrochemistry. The nonlinear optical properties of the ruthenium(II) complexes were investigated by Z-scan techniques with 12 ns laser pulse at 540 nm, and all of them exhibit both nonlinear optical (NLO) absorption and self-defocusing effect. The corresponding effective NLO susceptibility |χ 3| of the complexes is in the range of 2.68×10 -12-4.57×10 -12 esu.
