FOr the integrable system with u(p, q) reduction, there is a well-known sufficient conditionto choose the parameters: the spectral parameters only take two mutually conjugate valuesand the solutions of the Lax pair sh...FOr the integrable system with u(p, q) reduction, there is a well-known sufficient conditionto choose the parameters: the spectral parameters only take two mutually conjugate valuesand the solutions of the Lax pair should satisfy certain orthogonal relations. In this paper, theauthor proves that, for the AKNS system, the Kaup-Newed system and the principal chiralfield (PCF), this condition is also necessary for generic potentials with the u(p, q) reduction.FOr some other reductions, sufficiency and necessity of more constraints are proved.展开更多
The thermal properties of photonic crystal fiber(PCF) laser with 18 circularly distributed cores are investigated by using full-vector finite element method(FEM).The results show that the 18-core PCF has a more effect...The thermal properties of photonic crystal fiber(PCF) laser with 18 circularly distributed cores are investigated by using full-vector finite element method(FEM).The results show that the 18-core PCF has a more effective thermal dispersion construction compared with the single core PCF and 19-core PCF.In addition,the temperature distribution of 18-core PCF laser with different thermal loads is simulated.The results show that the core temperature approaches the fiber drawing value of 1800 K approximately when the thermal load is above 80 W/m which corresponds to the pumping power of 600 W approximately,while the coating temperature approaches the damage value of about 550 K when the thermal load is above 15 W/m which corresponds to the pumping power of 110 W approximately.Therefore the fiber cooling is necessary to achieve power scaling.Compared with other different cooling systems,the copper cooling scheme is found to be an effective method to reduce the thermal effects.展开更多
文摘FOr the integrable system with u(p, q) reduction, there is a well-known sufficient conditionto choose the parameters: the spectral parameters only take two mutually conjugate valuesand the solutions of the Lax pair should satisfy certain orthogonal relations. In this paper, theauthor proves that, for the AKNS system, the Kaup-Newed system and the principal chiralfield (PCF), this condition is also necessary for generic potentials with the u(p, q) reduction.FOr some other reductions, sufficiency and necessity of more constraints are proved.
基金supported by the National Basic Research Program of China(No.2010CB327801)the Key Program of National Natural Science Foundation of China(No.60637010)the Natural Science Research Project in University of Hebei Province(No.Z2010163)
文摘The thermal properties of photonic crystal fiber(PCF) laser with 18 circularly distributed cores are investigated by using full-vector finite element method(FEM).The results show that the 18-core PCF has a more effective thermal dispersion construction compared with the single core PCF and 19-core PCF.In addition,the temperature distribution of 18-core PCF laser with different thermal loads is simulated.The results show that the core temperature approaches the fiber drawing value of 1800 K approximately when the thermal load is above 80 W/m which corresponds to the pumping power of 600 W approximately,while the coating temperature approaches the damage value of about 550 K when the thermal load is above 15 W/m which corresponds to the pumping power of 110 W approximately.Therefore the fiber cooling is necessary to achieve power scaling.Compared with other different cooling systems,the copper cooling scheme is found to be an effective method to reduce the thermal effects.
