Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of...Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schr¨odinger(NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.展开更多
Using an adaptive split-step Fourier method,the coupled nonlinear Schrdinger equations have been numerically solved in this paper.The nonlinear propagation of an ultrashort optical pulse in the birefringent photonic c...Using an adaptive split-step Fourier method,the coupled nonlinear Schrdinger equations have been numerically solved in this paper.The nonlinear propagation of an ultrashort optical pulse in the birefringent photonic crystal fibers is investigated numerically.It is found that the phenomenon of pulse trapping occurs when the incident pulse is deviating from the principal axis of the fiber with some angle.Owing to the birefringence effect,the incident pulse can be regarded as two orthogonal polarized pulses.The phenomenon of pulse trapping occurs because of the cross phase modulation(XPM) between the two components.As a result,the bandwidth of the supercontinuum(SC) decreases compared with the case that the incident pulse is input along the principal axis.When the polarization direction of the incident pulse is parallel to the fast axis,the bandwidth of the supercontinuum is maximal.展开更多
The authors study the compressible limit of the nonlinear Schrdinger equation with different-degree small parameter nonlinearities in small time for initial data with Sobolev regularity before the formation of singula...The authors study the compressible limit of the nonlinear Schrdinger equation with different-degree small parameter nonlinearities in small time for initial data with Sobolev regularity before the formation of singularities in the limit system.On the one hand,the existence and uniqueness of the classical solution are proved for the dispersive perturbation of the quasi-linear symmetric system corresponding to the initial value problem of the above nonlinear Schrdinger equation.On the other hand,in the limit system,it is shown that the density converges to the solution of the compressible Euler equation and the validity of the WKB expansion is justified.展开更多
基金Supported by the Research Grants Council contract HKU17200815
文摘Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schr¨odinger(NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.
基金supported by the National Natural Science Foundation of China (No.10874145)the Natural Science Foundation of Hebei Province of China (No.F2009000481)the China Postdoctoral Science Foundation (No.20080440014)
文摘Using an adaptive split-step Fourier method,the coupled nonlinear Schrdinger equations have been numerically solved in this paper.The nonlinear propagation of an ultrashort optical pulse in the birefringent photonic crystal fibers is investigated numerically.It is found that the phenomenon of pulse trapping occurs when the incident pulse is deviating from the principal axis of the fiber with some angle.Owing to the birefringence effect,the incident pulse can be regarded as two orthogonal polarized pulses.The phenomenon of pulse trapping occurs because of the cross phase modulation(XPM) between the two components.As a result,the bandwidth of the supercontinuum(SC) decreases compared with the case that the incident pulse is input along the principal axis.When the polarization direction of the incident pulse is parallel to the fast axis,the bandwidth of the supercontinuum is maximal.
基金Project supported by the National Natural Science Foundation of China (Nos.10801102,10771151)the Sichuan Youth Sciences and Technology Foundation (No.07ZQ026-009)the China Postdoctoral Science Foundation
文摘The authors study the compressible limit of the nonlinear Schrdinger equation with different-degree small parameter nonlinearities in small time for initial data with Sobolev regularity before the formation of singularities in the limit system.On the one hand,the existence and uniqueness of the classical solution are proved for the dispersive perturbation of the quasi-linear symmetric system corresponding to the initial value problem of the above nonlinear Schrdinger equation.On the other hand,in the limit system,it is shown that the density converges to the solution of the compressible Euler equation and the validity of the WKB expansion is justified.
