The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich e...The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich explicit and exact travelling wave solutions,which contain solitary-wave solutions,periodic solutions,and combined formal solitary-wave solutions,are obtained.展开更多
There are often system. The high measure many inter-harmonics in power t accuracy of inter-harmonics order, amplitude and initial phase is needed. A new approach is presented for inter-harmonic modeling and parameter ...There are often system. The high measure many inter-harmonics in power t accuracy of inter-harmonics order, amplitude and initial phase is needed. A new approach is presented for inter-harmonic modeling and parameter estimation based on linear support vector machine （SVM）. Firstly, parameter estimation of linear model is realized based on standard linear SVM. Then, interharmonic model is transformed to a linear model according to trigonometric functions. The approach obtains order of inter-harmonic model with windowed Blackman-Tukey （BT） spectrum analysis, and gets number and frequency of harmonics. Finally, the linear SVM is applied to estimate the inter-harmonic parameters, amplitude and initial phase. The simulation results show that the proposed approach has high precision and good antinoise. The accuracy of three parameters are all higher than 98%.展开更多
In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the （2＋1）-dimensional variable coefficients Broer-Kaup （VCBK） equations. The...In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the （2＋1）-dimensional variable coefficients Broer-Kaup （VCBK） equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.展开更多
In this paper,by improving some procedure of extended tanh-function method,some new exact solutions to the integrable Broer-Kaup equations in(2 + 1)-dimensional spaces are obtained,which include soliton-like solutions...In this paper,by improving some procedure of extended tanh-function method,some new exact solutions to the integrable Broer-Kaup equations in(2 + 1)-dimensional spaces are obtained,which include soliton-like solutions,solitary wave solutions,trigonometric function solutions,and rational solutions.展开更多
In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with thr...In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with threearbitrary functions are obtained including hyperbolic function solutions,trigonometric function solutions,and rationalsolutions.This method can be applied to other higher-dimensional nonlinear partial differential equations.展开更多
With the help of an objective reduction approach （ORA）, abundant exact solutions of （2＋1）-dimensional higher-order Boussinesq system （including some hyperboloid function solutions, trigonometric function solutio...With the help of an objective reduction approach （ORA）, abundant exact solutions of （2＋1）-dimensional higher-order Boussinesq system （including some hyperboloid function solutions, trigonometric function solutions, and a rational function solution） are obtained. It is shown that some novel soliton structures, like single linearity soliton structure, breath soliton structure, single linearity y-periodic solitary wave structure, libration dromion structure, and kink-like multisoliton structure with actual physical meaning exist in the （2＋1）-dimensional higher-order Boussinesq system.展开更多
This paper studies the Generalized Bretherton equation using trigonometric function method including the sech-function method, the sine-cosine function method, and the tanh-function method, and He＇s semi-inverse meth...This paper studies the Generalized Bretherton equation using trigonometric function method including the sech-function method, the sine-cosine function method, and the tanh-function method, and He＇s semi-inverse method （He＇s variational method）. Various traveling wave solutions are obtained, revealing an intrinsic relationship among the amplitude, frequency, and wave speed.展开更多
Based on the teleseismic waveform data recorded by 82 permanent broadband stations in Guangdong Province and its adjacent areas including Fujian, Jiangxi, Hunan, Guangxi, Hainan and Taiwan, we calculate body wave rece...Based on the teleseismic waveform data recorded by 82 permanent broadband stations in Guangdong Province and its adjacent areas including Fujian, Jiangxi, Hunan, Guangxi, Hainan and Taiwan, we calculate body wave receiver functions under all stations, and obtain the crustal thickness and average Poisson＇s ratio beneath all stations by the H-K stacking-search method of receiver function. The results show that the crustal thickness with an average thickness of 29. 5km in Guangdong Province and its adjacent areas ranges between 26. 8km and 33. 6kin and gradually thins from northwest to southeast. The crustal thickness in the Zhujiang Delta, western Guangdong, Nanning and Nan＇ao areas is relatively thinner and ranges between 25. 0km and 28. 0km. The minimum crustal thickness is about 26km beneath Wengtian, Hainan and the Zhanjiang zone and Shangchuan Island in Guangdong. The crustal thickness in the zones of Mingxi, Fujian and Yongzhou, Hunan is thicker and varies between 31.0km and 34.0km. The distribution of Poisson＇s ratio in our study region ranges between 0.20 and 0. 29. Poisson＇s ratios in Southeast Hainan, the coastal areas of East Guangdong and West Fujian and the South Jiangxi have distinctly higher values than in others. It suggests that the various geothermal fields located in these areas have high heat flow values. The distribution of crustal thickness and Poisson＇s ratio has an obvious block feature and may be related to the distribution of faults and historical earthquakes.展开更多
In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditio...In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditions. Some periodic wave and smooth solitary wave solutions of the equation are obtained. Moreover, we find some new hyperbolic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points.展开更多
The simplest spin-orbital model can host a nematic spin-orbital liquid state on the triangular lattice.We provide clear evidence that the ground state of the SU(4)Kugel-Khomskii model on the triangular lattice can be ...The simplest spin-orbital model can host a nematic spin-orbital liquid state on the triangular lattice.We provide clear evidence that the ground state of the SU(4)Kugel-Khomskii model on the triangular lattice can be well described by a‘‘single”Gutzwiller projected wave function with an emergent parton Fermi surface,despite it exhibits strong finite-size effect in quasi-one-dimensional cylinders.The finite-size effect can be resolved by the fact that the parton Fermi surface consists of open orbits in the reciprocal space.Thereby,a stripy liquid state is expected in the two-dimensional limit,which preserves the SU(4)symmetry while breaks the translational symmetry by doubling the unit cell along one of the lattice vector directions.It is indicative that these stripes are critical and the central charge is c=3,in agreement with the SU(4)1Wess-Zumino-Witten conformal field theory.All these results are consistent with the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem.展开更多
文摘The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich explicit and exact travelling wave solutions,which contain solitary-wave solutions,periodic solutions,and combined formal solitary-wave solutions,are obtained.
基金National Natural Science Foundation of China(No.60774011)Natural Science Foundation of zhejiang Province,China(No.Y1090182)
文摘There are often system. The high measure many inter-harmonics in power t accuracy of inter-harmonics order, amplitude and initial phase is needed. A new approach is presented for inter-harmonic modeling and parameter estimation based on linear support vector machine （SVM）. Firstly, parameter estimation of linear model is realized based on standard linear SVM. Then, interharmonic model is transformed to a linear model according to trigonometric functions. The approach obtains order of inter-harmonic model with windowed Blackman-Tukey （BT） spectrum analysis, and gets number and frequency of harmonics. Finally, the linear SVM is applied to estimate the inter-harmonic parameters, amplitude and initial phase. The simulation results show that the proposed approach has high precision and good antinoise. The accuracy of three parameters are all higher than 98%.
基金The project supported by National Natural Science Foundation of China undcr Grant No. 10172056 .
文摘In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the （2＋1）-dimensional variable coefficients Broer-Kaup （VCBK） equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found.
文摘In this paper,by improving some procedure of extended tanh-function method,some new exact solutions to the integrable Broer-Kaup equations in(2 + 1)-dimensional spaces are obtained,which include soliton-like solutions,solitary wave solutions,trigonometric function solutions,and rational solutions.
基金Supported by the Natural Science Foundation of Shanghai under Grant No.09ZR1410800the Science Foundation of Key Laboratory of Mathematics Mechanization under Grant No.KLMM0806+1 种基金the Shanghai Leading Academic Discipline Project under Grant No.J50101Key Disciplines of Shanghai Municipality under Grant No.S30104
文摘In this paper,we construct exact solutions for the (2+1)-dimensional Boiti-Leon-Pempinelle equation byusing the (G'/G)-expansion method,and with the help of Maple.As a result,non-travelling wave solutions with threearbitrary functions are obtained including hyperbolic function solutions,trigonometric function solutions,and rationalsolutions.This method can be applied to other higher-dimensional nonlinear partial differential equations.
基金the Natural Science Foundation of Zhejiang Province under Grant Nos. Y604106 and Y606181the Foundation of New Century "151 Talent Engineering" of Zhejiang Province+1 种基金the Scientific Research Foundation of Key Discipline of Zhejiang Provincethe Natural Science Foundation of Zhejiang Lishui University under Grant No. KZ06002
文摘With the help of an objective reduction approach （ORA）, abundant exact solutions of （2＋1）-dimensional higher-order Boussinesq system （including some hyperboloid function solutions, trigonometric function solutions, and a rational function solution） are obtained. It is shown that some novel soliton structures, like single linearity soliton structure, breath soliton structure, single linearity y-periodic solitary wave structure, libration dromion structure, and kink-like multisoliton structure with actual physical meaning exist in the （2＋1）-dimensional higher-order Boussinesq system.
文摘This paper studies the Generalized Bretherton equation using trigonometric function method including the sech-function method, the sine-cosine function method, and the tanh-function method, and He＇s semi-inverse method （He＇s variational method）. Various traveling wave solutions are obtained, revealing an intrinsic relationship among the amplitude, frequency, and wave speed.
基金sponsored by the Science and Technology Program of Guangdong Province(20090308)
文摘Based on the teleseismic waveform data recorded by 82 permanent broadband stations in Guangdong Province and its adjacent areas including Fujian, Jiangxi, Hunan, Guangxi, Hainan and Taiwan, we calculate body wave receiver functions under all stations, and obtain the crustal thickness and average Poisson＇s ratio beneath all stations by the H-K stacking-search method of receiver function. The results show that the crustal thickness with an average thickness of 29. 5km in Guangdong Province and its adjacent areas ranges between 26. 8km and 33. 6kin and gradually thins from northwest to southeast. The crustal thickness in the Zhujiang Delta, western Guangdong, Nanning and Nan＇ao areas is relatively thinner and ranges between 25. 0km and 28. 0km. The minimum crustal thickness is about 26km beneath Wengtian, Hainan and the Zhanjiang zone and Shangchuan Island in Guangdong. The crustal thickness in the zones of Mingxi, Fujian and Yongzhou, Hunan is thicker and varies between 31.0km and 34.0km. The distribution of Poisson＇s ratio in our study region ranges between 0.20 and 0. 29. Poisson＇s ratios in Southeast Hainan, the coastal areas of East Guangdong and West Fujian and the South Jiangxi have distinctly higher values than in others. It suggests that the various geothermal fields located in these areas have high heat flow values. The distribution of crustal thickness and Poisson＇s ratio has an obvious block feature and may be related to the distribution of faults and historical earthquakes.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11161013,11361017,and 11301106Foundation of Guangxi Key Lab of Trusted Software and Program for Innovative Research Team of Guilin University of Electronic TechnologyProject of Outstanding Young Teachers’Training in Higher Education Institutions of Guangxi
文摘In this letter, we investigate traveling wave solutions of a nonlinear wave equation with degenerate dispersion. The phase portraits of corresponding traveling wave system are given under different parametric conditions. Some periodic wave and smooth solitary wave solutions of the equation are obtained. Moreover, we find some new hyperbolic function compactons instead of well-known trigonometric function compactons by analyzing nilpotent points.
基金supported by the National Natural Science Foundation of China(12034004 and 11774306)the K.C.Wong Education Foundation(GJTD2020–01)+3 种基金the Strategic Priority Research Program of Chinese Academy of Sciences(XDB28000000)funded by the European Research Council(ERC)under the European Unions Horizon 2020 Research and Innovation Program(771537)supported by the Deutsche Forschungsgemeinschaft through project A06 of SFB 1143(247310070)The numerical simulations in this work are based on the GraceQ project(www.gracequantum.org)。
文摘The simplest spin-orbital model can host a nematic spin-orbital liquid state on the triangular lattice.We provide clear evidence that the ground state of the SU(4)Kugel-Khomskii model on the triangular lattice can be well described by a‘‘single”Gutzwiller projected wave function with an emergent parton Fermi surface,despite it exhibits strong finite-size effect in quasi-one-dimensional cylinders.The finite-size effect can be resolved by the fact that the parton Fermi surface consists of open orbits in the reciprocal space.Thereby,a stripy liquid state is expected in the two-dimensional limit,which preserves the SU(4)symmetry while breaks the translational symmetry by doubling the unit cell along one of the lattice vector directions.It is indicative that these stripes are critical and the central charge is c=3,in agreement with the SU(4)1Wess-Zumino-Witten conformal field theory.All these results are consistent with the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem.
