In the past few decades, the （1 ＋ 1）-dimensional nonlinear Schr6dinger （NLS） equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the de...In the past few decades, the （1 ＋ 1）-dimensional nonlinear Schr6dinger （NLS） equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the （1＋1）-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new （2＋1）-dimensional multiscale transform, we derive the （2＋1）-dimensional dissipation nonlinear Schrodinger equation （DNLS） to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of （2＋ 1）-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the （2＋ 1）-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.展开更多
Studied in this paper is a(2+1)-dimensional coupled nonlinear Schr?dinger system with variable coefficients,which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifie...Studied in this paper is a(2+1)-dimensional coupled nonlinear Schr?dinger system with variable coefficients,which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. According to the similarity transformation, we derive the type-Ⅰ and type-Ⅱ rogue-wave solutions. We graphically present two types of the rouge wave and discuss the influence of the diffraction parameter on the rogue waves.When the diffraction parameters are exponentially-growing-periodic, exponential, linear and quadratic parameters, we obtain the periodic rogue wave and composite rogue waves respectively.展开更多
In order to solve the problem of truncating the open boundaries of cylindrical waveguides used in the simulation of high power microwave （HPM） sources, this paper studies the convolutional PML （CPML） in the cylind...In order to solve the problem of truncating the open boundaries of cylindrical waveguides used in the simulation of high power microwave （HPM） sources, this paper studies the convolutional PML （CPML） in the cylindrical coordinate system. The electromagnetic field＇s FDTD equations and the expressions of axis boundary conditions are presented. Numerical experiments are conducted to validate the equations and axis boundary conditions. The performance of CPML is simulated when it is used to truncate the cylindrical waveguides excited by the sources with different frequencies and modes in the 2.5-dimensional problems. Numerical results show that the maximum relative errors are all less than -90 dB. The CPML method is introduced in the 2.5-dimensional electromagnetic PIC software, and the relativistic backward wave oscillator is simulated by using this method. The results show that the property of CPML is much better than that of the Mur-type absorbing boundary condition when they are used to truncate the open boundaries of waveguides. The CPML is especially suitable for truncating the open boundaries of the dispersive waveguide devices in the simulation of HPM sources.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.41406018)
文摘In the past few decades, the （1 ＋ 1）-dimensional nonlinear Schr6dinger （NLS） equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the （1＋1）-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new （2＋1）-dimensional multiscale transform, we derive the （2＋1）-dimensional dissipation nonlinear Schrodinger equation （DNLS） to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of （2＋ 1）-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the （2＋ 1）-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11772017,11272023,and 11471050the Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications),China(IPOC:2017ZZ05)the Fundamental Research Funds for the Central Universities of China under Grant No.2011BUPTYB02
文摘Studied in this paper is a(2+1)-dimensional coupled nonlinear Schr?dinger system with variable coefficients,which describes the propagation of an optical beam inside the two-dimensional graded-index waveguide amplifier with the polarization effects. According to the similarity transformation, we derive the type-Ⅰ and type-Ⅱ rogue-wave solutions. We graphically present two types of the rouge wave and discuss the influence of the diffraction parameter on the rogue waves.When the diffraction parameters are exponentially-growing-periodic, exponential, linear and quadratic parameters, we obtain the periodic rogue wave and composite rogue waves respectively.
文摘In order to solve the problem of truncating the open boundaries of cylindrical waveguides used in the simulation of high power microwave （HPM） sources, this paper studies the convolutional PML （CPML） in the cylindrical coordinate system. The electromagnetic field＇s FDTD equations and the expressions of axis boundary conditions are presented. Numerical experiments are conducted to validate the equations and axis boundary conditions. The performance of CPML is simulated when it is used to truncate the cylindrical waveguides excited by the sources with different frequencies and modes in the 2.5-dimensional problems. Numerical results show that the maximum relative errors are all less than -90 dB. The CPML method is introduced in the 2.5-dimensional electromagnetic PIC software, and the relativistic backward wave oscillator is simulated by using this method. The results show that the property of CPML is much better than that of the Mur-type absorbing boundary condition when they are used to truncate the open boundaries of waveguides. The CPML is especially suitable for truncating the open boundaries of the dispersive waveguide devices in the simulation of HPM sources.
