The present study revisited the first two leading modes of tropical Pacific sea surface temperature anomalies （SSTA） during the period of 1979-2008. It is suggested that the so-called El Nino Modoki, which is captur...The present study revisited the first two leading modes of tropical Pacific sea surface temperature anomalies （SSTA） during the period of 1979-2008. It is suggested that the so-called El Nino Modoki, which is captured by the second mode, exists objectively and exhibits obvious differences from traditional El Nifio, which is captured by the first mode, in terms of its spatial characteristics. Furthermore, the authors found that El Nino Modoki is linearly independent of traditional El Nino; hence, it cannot be described as part of the traditional El Nino evolution, and vice versa.展开更多
In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plas...In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the （3＋1）-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the （3＋1）-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.展开更多
A model of vibrating device coupling two pendulums (VDP) which is highly nonlinear was put forward to conduct vibration analysis. Based on energy analysis, dynamic equations with cubic nonlinearities were established ...A model of vibrating device coupling two pendulums (VDP) which is highly nonlinear was put forward to conduct vibration analysis. Based on energy analysis, dynamic equations with cubic nonlinearities were established using Lagrange's equation. In order to obtain approximate solution, multiple time scales method, one of perturbation technique, was applied. Cases of non-resonant and 1:1:2:2 internal resonant were discussed. In the non-resonant case, the validity of multiple time scales method is confirmed, comparing numerical results derived from fourth order Runge-Kutta method with analytical results derived from first order approximate expression. In the 1:1:2:2 internal resonant case, modal amplitudes of Aa1 and Ab2 increase, respectively, from 0.38 to 0.63 and from 0.19 to 0.32, while the corresponding frequencies have an increase of almost 1.6 times with changes of initial conditions, indicating the existence of typical nonlinear phenomenon. In addition, the chaotic motion is found under this condition.展开更多
Recently,there are two independent approaches related to a class of nonlinear Lie algebras of three generators;and the realizations of these generators are achieved respectively in Schwinger-boson and position represe...Recently,there are two independent approaches related to a class of nonlinear Lie algebras of three generators;and the realizations of these generators are achieved respectively in Schwinger-boson and position representation.However,by use of the representation transformation between these two representations,the equivalence of the two realizations is therefore proved.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 40975029,40675028,and 40810059005)
文摘The present study revisited the first two leading modes of tropical Pacific sea surface temperature anomalies （SSTA） during the period of 1979-2008. It is suggested that the so-called El Nino Modoki, which is captured by the second mode, exists objectively and exhibits obvious differences from traditional El Nifio, which is captured by the first mode, in terms of its spatial characteristics. Furthermore, the authors found that El Nino Modoki is linearly independent of traditional El Nino; hence, it cannot be described as part of the traditional El Nino evolution, and vice versa.
基金Supported by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos. 20060006024 and 20080013006Chinese Ministry of Education, by the National Natural Science Foundation of China under Grant No. 60772023+2 种基金by the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. SKLSDE-07-001Beijing University of Aeronautics and Astronauticsby the National Basic Research Program of China (973 Program) under Grant No. 2005CB321901
文摘In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the （3＋1）-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the （3＋1）-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.
基金Projects(50574091, 50774084) supported by the National Natural Science Foundation of ChinaProject supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions+1 种基金Project(CXLX12_0949) supported by Research and Innovation Project for College Graduates of Jiangsu Province, ChinaProject(2013DXS03) supported by the Fundamental Research Funds for the Central Universities, China
文摘A model of vibrating device coupling two pendulums (VDP) which is highly nonlinear was put forward to conduct vibration analysis. Based on energy analysis, dynamic equations with cubic nonlinearities were established using Lagrange's equation. In order to obtain approximate solution, multiple time scales method, one of perturbation technique, was applied. Cases of non-resonant and 1:1:2:2 internal resonant were discussed. In the non-resonant case, the validity of multiple time scales method is confirmed, comparing numerical results derived from fourth order Runge-Kutta method with analytical results derived from first order approximate expression. In the 1:1:2:2 internal resonant case, modal amplitudes of Aa1 and Ab2 increase, respectively, from 0.38 to 0.63 and from 0.19 to 0.32, while the corresponding frequencies have an increase of almost 1.6 times with changes of initial conditions, indicating the existence of typical nonlinear phenomenon. In addition, the chaotic motion is found under this condition.
基金Supported by National Natural Science Foundation of China under Grant No. 11175063
文摘Recently,there are two independent approaches related to a class of nonlinear Lie algebras of three generators;and the realizations of these generators are achieved respectively in Schwinger-boson and position representation.However,by use of the representation transformation between these two representations,the equivalence of the two realizations is therefore proved.
