In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation...In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.展开更多
In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, ...In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, the （2＋1）-dimensional Lax pair is reduced to （1＋1）-dimensional Lax pair, whose compatibility yields the reduction of the ANNV equation. Based on the obtained reductions of the ANNV equation, a lot of new exact solutions for the ANNV equation are found. This shows that for an integrable system, both the symmetry and the reductions can be obtained through its corresponding Lax pair.展开更多
In this paper, the generalized ranch function method is extended to （2＋1）-dimensianal canonical generalized KP （CGKP） equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit ...In this paper, the generalized ranch function method is extended to （2＋1）-dimensianal canonical generalized KP （CGKP） equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the （2＋1）-dimensional OGKP equation with variable coetffcients.展开更多
A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, th...A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.展开更多
Using the classical Lie method of infinitesimals, we first obtain the symmetry of the （2＋1）-dimensional Burgers-Korteweg-de-Vries （3D-BKdV） equation. Then we reduce the 3D-BKdV equation using the symmetry and giv...Using the classical Lie method of infinitesimals, we first obtain the symmetry of the （2＋1）-dimensional Burgers-Korteweg-de-Vries （3D-BKdV） equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation.展开更多
With the aid of computerized symbolic computation and Riccati equation rational expansion approach, some new and more general rational formal solutions to （2＋1）-dimensional Toda system are obtained. The method used...With the aid of computerized symbolic computation and Riccati equation rational expansion approach, some new and more general rational formal solutions to （2＋1）-dimensional Toda system are obtained. The method used here can also be applied to solve other nonlinear differential-difference equation or equations.展开更多
We propose two simple ansaetze that allow us to obtain different analytical solutions for two generalizeal versions of the nonlinear Schrodinger equation, such as the averaged dispersive-managed fiber system equation ...We propose two simple ansaetze that allow us to obtain different analytical solutions for two generalizeal versions of the nonlinear Schrodinger equation, such as the averaged dispersive-managed fiber system equation and the extended nonlinear Schrodinger equation which describe the femtosecond pulse propagation in monomode optical fiber. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media.展开更多
We propose a dispersion flattened fiber (DFF) front-haul transmission system with high bitrate, polarization multiplexing (PM) and quadrature amplitude modulation (QAM) signal at low input optical power. The modulatio...We propose a dispersion flattened fiber (DFF) front-haul transmission system with high bitrate, polarization multiplexing (PM) and quadrature amplitude modulation (QAM) signal at low input optical power. The modulation format of the system is PM-16 QAM, and the bitrate is 256 Gbit/s. The transmission characteristics over DFF link system are experimentally studied, which are compared with those over non-zero dispersion shifted fiber (NZDSF) link and standard single mode fiber (SSMF) link. The experimental results show that the error vector magnitude(EVM) of 256 Gbit/s and PM-16 QAM signal over 25 km DFF link is 0.75% better than that over 25 km NZDSF link at least, and the bit error rate (BER) and Q-factor are much better than those of NZDSF. Their EVM and BER are both decreased with the increase of input optical power, and the Q-factor is increased. Those characteristics over 25 km SSMF are the worst at the same case. The larger the dispersion is, the more the constellation points are deviated from their respective centers and the worse the constellation characteristics are. The greater the attenuation of the DFF is, the smaller the input power of the DFF is, the more the constellation points are deviated from their centers and the worse the constellation characteristics are. This study provides a new idea and experimental support for long span front-haul propagation in mobile communication.展开更多
A graded-index mode division multiplexer with low loss and low crosstalk is proposed. The transmission channel adopts a pure silica core with large effective area to achieve low attenuation, which effectively reduces ...A graded-index mode division multiplexer with low loss and low crosstalk is proposed. The transmission channel adopts a pure silica core with large effective area to achieve low attenuation, which effectively reduces the splicing loss with pure silica core few-mode transmission fiber. Low differential mode group delay is realized by using graded-index distribution. Also the effective index difference of the modes is greater than 0.5×10-3 to ensure low crosstalk between modes. The performance of the mode division multiplexer is investigated using the beam propagation method and full-vector finite element method. The result shows that the coupling efficiency of multiplexer is better than-0.479 dB, and the extinction ratio is higher than 31.2 dB in the wavelength of 1 400—1 700 nm. In C band, the average coupling efficiency of all mode channels of multiplexer is better than that of-0.140 dB, which shows flatness. The proposed scheme is an effective way to implement a multiplexer with low crosstalk, low los s, low fusion loss, high coupling efficiency, high extinction ratio and wide operating band.展开更多
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the modified CK＇s direct method to find symmetry groups of nonlinear partial differential equation is extended to （2＋1）-dimensional variable coeffficient canonical generalized KP （VCCGKP） equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation.
基金Natural Science Foundation of Shandong Province under Grant Nos.2004zx16 and Q2005A01
文摘In this paper, the direct symmetry method is extended to the Lax pair of the ANNV equation. As a result, symmetries of the Lax pair and the ANNV equation are obtained at the same time. Applying the obtained symmetry, the （2＋1）-dimensional Lax pair is reduced to （1＋1）-dimensional Lax pair, whose compatibility yields the reduction of the ANNV equation. Based on the obtained reductions of the ANNV equation, a lot of new exact solutions for the ANNV equation are found. This shows that for an integrable system, both the symmetry and the reductions can be obtained through its corresponding Lax pair.
基金The project supported by the Natural Science Foundation of Shandong Province under Grant Nos. 2004zx16 and Q2005A01
文摘In this paper, the generalized ranch function method is extended to （2＋1）-dimensianal canonical generalized KP （CGKP） equation with variable coetfficients. Taking advantage of the Riccati equation, many explicit exact solutions, which contain multiple soliton-like and periodic solutions, are obtained for the （2＋1）-dimensional OGKP equation with variable coetffcients.
文摘A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004 zx 16
文摘Using the classical Lie method of infinitesimals, we first obtain the symmetry of the （2＋1）-dimensional Burgers-Korteweg-de-Vries （3D-BKdV） equation. Then we reduce the 3D-BKdV equation using the symmetry and give some exact solutions of the 3D-BKdV equation. When using the direct method, we restrict a condition and get a relationship between the new solutions and the old ones. Given a solution of the 3D-BKdV equation, we can get a new one from the relationship. The relationship between the symmetry obtained by using the classical Lie method and that obtained by using the direct method is also mentioned. At last, we give the conservation laws of the 3D-BKdV equation.
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province.
文摘With the aid of computerized symbolic computation and Riccati equation rational expansion approach, some new and more general rational formal solutions to （2＋1）-dimensional Toda system are obtained. The method used here can also be applied to solve other nonlinear differential-difference equation or equations.
基金The project supported by National Natural Science Foundation of China and the Natural Science Foundation of Shandong Province of China
文摘We propose two simple ansaetze that allow us to obtain different analytical solutions for two generalizeal versions of the nonlinear Schrodinger equation, such as the averaged dispersive-managed fiber system equation and the extended nonlinear Schrodinger equation which describe the femtosecond pulse propagation in monomode optical fiber. Among these solutions we can find solitary wave and periodic wave solutions representing the propagation of different waveforms in nonlinear media.
基金supported by the National Natural Science Foundation of China(Nos.61671227,61431009 and 61501213)the Shandong Provincial Natural Science Foundation(No.ZR2011FM015)Taishan Scholar Research Fund of Shandong Province
文摘We propose a dispersion flattened fiber (DFF) front-haul transmission system with high bitrate, polarization multiplexing (PM) and quadrature amplitude modulation (QAM) signal at low input optical power. The modulation format of the system is PM-16 QAM, and the bitrate is 256 Gbit/s. The transmission characteristics over DFF link system are experimentally studied, which are compared with those over non-zero dispersion shifted fiber (NZDSF) link and standard single mode fiber (SSMF) link. The experimental results show that the error vector magnitude(EVM) of 256 Gbit/s and PM-16 QAM signal over 25 km DFF link is 0.75% better than that over 25 km NZDSF link at least, and the bit error rate (BER) and Q-factor are much better than those of NZDSF. Their EVM and BER are both decreased with the increase of input optical power, and the Q-factor is increased. Those characteristics over 25 km SSMF are the worst at the same case. The larger the dispersion is, the more the constellation points are deviated from their respective centers and the worse the constellation characteristics are. The greater the attenuation of the DFF is, the smaller the input power of the DFF is, the more the constellation points are deviated from their centers and the worse the constellation characteristics are. This study provides a new idea and experimental support for long span front-haul propagation in mobile communication.
基金supported by the National Natural Science Foundation of China(Nos.61671227 and 61431009)the Shandong Provincial Natural Science Foundation(No.ZR2011FM015)the Taishan Scholar Research Fund of Shandong Province
文摘A graded-index mode division multiplexer with low loss and low crosstalk is proposed. The transmission channel adopts a pure silica core with large effective area to achieve low attenuation, which effectively reduces the splicing loss with pure silica core few-mode transmission fiber. Low differential mode group delay is realized by using graded-index distribution. Also the effective index difference of the modes is greater than 0.5×10-3 to ensure low crosstalk between modes. The performance of the mode division multiplexer is investigated using the beam propagation method and full-vector finite element method. The result shows that the coupling efficiency of multiplexer is better than-0.479 dB, and the extinction ratio is higher than 31.2 dB in the wavelength of 1 400—1 700 nm. In C band, the average coupling efficiency of all mode channels of multiplexer is better than that of-0.140 dB, which shows flatness. The proposed scheme is an effective way to implement a multiplexer with low crosstalk, low los s, low fusion loss, high coupling efficiency, high extinction ratio and wide operating band.
