In this paper, an algorithm is proposed to solve the 0（2） symmetric positive solutions to the boundary value problem of the p-Henon equation. Taking 1 in the p- Henon equation as a bifurcation parameter, the symmetr...In this paper, an algorithm is proposed to solve the 0（2） symmetric positive solutions to the boundary value problem of the p-Henon equation. Taking 1 in the p- Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation point on the branch of the O（2） symmetric positive solutions is found via the extended systems. The other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.展开更多
Provides information on a study which proposed a continuation method for switching solution branches at a pitchfork point. Problem of the standard pitchfork; Information on the systems of equations; Numerical examples...Provides information on a study which proposed a continuation method for switching solution branches at a pitchfork point. Problem of the standard pitchfork; Information on the systems of equations; Numerical examples of the efficiency of the proposed switching method.展开更多
Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the...Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.展开更多
A switchable dual-wavelength erbium-doped fiber laser(EDFL) with tunable wavelength is demonstrated. The ring cavity consists of two branches with a fiber Bragg grating(FBG) and a spherical-shape structure as fiber fi...A switchable dual-wavelength erbium-doped fiber laser(EDFL) with tunable wavelength is demonstrated. The ring cavity consists of two branches with a fiber Bragg grating(FBG) and a spherical-shape structure as fiber filters, respectively. By adjusting the variable optical attenuator(VOA), the laser can be switched between the single-wavelength mode and the dual-wavelength mode. The spherical-shape structure has good sensitivity to the temperature. When the temperature changes from 30 °C to 190 °C, the central wavelength of the EDFL generated by the branch of spherical-shape structure varies from 1 551.6 nm to 1 561.8 nm, which means that the wavelength interval is tunable.展开更多
基金Project supported by the National Natural Science Foundation of China (No. 10901106)the Shanghai Leading Academic Discipline Project (No. S30405)+2 种基金the Shanghai Normal University Academic Project (No. SK200936)the Natural Science Foundation of Shanghai (No. 09ZR1423200)the Innovation Program of Shanghai Municipal Education Commission (No. 09YZ150)
文摘In this paper, an algorithm is proposed to solve the 0（2） symmetric positive solutions to the boundary value problem of the p-Henon equation. Taking 1 in the p- Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation point on the branch of the O（2） symmetric positive solutions is found via the extended systems. The other symmetric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.
基金NNSF of China, the Youth Science Foundation of Shanghai Higher Education(99QA80) and Science Foundation of Shanghai Science an
文摘Provides information on a study which proposed a continuation method for switching solution branches at a pitchfork point. Problem of the standard pitchfork; Information on the systems of equations; Numerical examples of the efficiency of the proposed switching method.
基金supported by the National Natural Science Foundation of China (Grant No. 10671130)the Science Foundation of Shanghai Municipal Education Commission (Grant No. 05DZ07)+2 种基金Shanghai Leading Academic Discipline Project (Grant No. T0401)Leading Foundation of Shanghai Science and Technology Commission (Grant No. 06JC14092)the Foundation of the Scientific Computing Key Laboratory of Shang-hai Universities
文摘Three algorithms based on the bifurcation method are applied to solving the D4 symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bi- furcation parameter, the D4-Σd(D4-Σ1, D4-Σ2) symmetry-breaking bifurcation points on the branch of the D4 symmetric positive solutions are found via the extended systems. Finally, Σd(Σ1, Σ2) sym- metric positive solutions are computed by the branch switching method based on the Liapunov-Schmidt reduction.
基金supported by the National High Technology Research and Development Program of China(No.2013AA014201)the Tianjin Youth Science Foundation(No.13JCQNJC01800)
文摘A switchable dual-wavelength erbium-doped fiber laser(EDFL) with tunable wavelength is demonstrated. The ring cavity consists of two branches with a fiber Bragg grating(FBG) and a spherical-shape structure as fiber filters, respectively. By adjusting the variable optical attenuator(VOA), the laser can be switched between the single-wavelength mode and the dual-wavelength mode. The spherical-shape structure has good sensitivity to the temperature. When the temperature changes from 30 °C to 190 °C, the central wavelength of the EDFL generated by the branch of spherical-shape structure varies from 1 551.6 nm to 1 561.8 nm, which means that the wavelength interval is tunable.
