A class of generalized complex Burgers equation is considered. First, a set of equations of the complex value functions are solved by using the homotopic mapping method. The approximate solution for the original gener...A class of generalized complex Burgers equation is considered. First, a set of equations of the complex value functions are solved by using the homotopic mapping method. The approximate solution for the original generalized complex Burgers equation is obtained. This method can find the approximation of arbitrary order of precision simply and reliably.展开更多
The E1 Nifio/La Nifia Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a coupled system of sea-air oscillator model is studied. ...The E1 Nifio/La Nifia Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a coupled system of sea-air oscillator model is studied. The aim is to create an asymptotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the method of homotopic mapping, the approximate solution of corresponding problem is studied. It is proven from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.展开更多
A reduces equation of the Kelvin wave is considered. By using the homotopic mapping solving method, the approximate solution is obtained. The homptopic mapping method is an analytic method, the obtained solution can a...A reduces equation of the Kelvin wave is considered. By using the homotopic mapping solving method, the approximate solution is obtained. The homptopic mapping method is an analytic method, the obtained solution can analyse operations sequentially.展开更多
This paper considers a class of oscillator for the El Nino/La Ninia-southern oscillation （ENSO） model. By using the homotopic mapping method, it obtains approximations of the solution for the ENSO model.
The EI Nimo and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. In this paper, an asymptotic method of solving nonlinear equations for the ENSO model i...The EI Nimo and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. In this paper, an asymptotic method of solving nonlinear equations for the ENSO model is proposed. And based on a class of oscillator of the ENSO model and by employing the method of homotopic mapping, the approximate solution of equations for the corresponding ENSO model is studied. It is proved from the results that homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for the ENSO model.展开更多
The thermally and wind-driven ocean circulation is a complicated natural phenomenon in the atmospheric physics. Hence we need to reduce it using basic models and solve the models using approximate methods. A non-linea...The thermally and wind-driven ocean circulation is a complicated natural phenomenon in the atmospheric physics. Hence we need to reduce it using basic models and solve the models using approximate methods. A non-linear model of the thermally and wind-driven ocean circulation is used in this paper. The results show that the zero solution of the linear equation is a stable focus point, which is the path curve trend origin point as time (t) trend to infinity. By using the homotopic mapping perturbation method, the exact solution of the model is obtained. The homotopic mapping perturbation method is an analytic solving method, so the obtained solution can be used for analytic operating sequentially. And then we can also obtain the diversified qualitative and quantitative behaviors for corresponding physical quantities.展开更多
A class of generalized Vakhnemko equation is considered. First, we solve the nonlinear differential equation by the homotopic mapping method. Then, an approximate soliton solution for the original generalized Vakhnemk...A class of generalized Vakhnemko equation is considered. First, we solve the nonlinear differential equation by the homotopic mapping method. Then, an approximate soliton solution for the original generalized Vakhnemko equation is obtained. By this method an arbitrary order approximation can be easily obtained and, similarly, approximate soliton solutions of other nonlinear equations can be acquired.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No. 40876010）, the Main Direction Program of the Knowledge Innovation Project of the Chinese Academy of Sciences （Grant No. KZCX2-YW-Q03-08）, the R ＆ D Special Fund for Public Welfare Industry （Meteorology） （Grant No. GYHY200806010）, the LASG State Key Laboratory Special Fund, the Foundation of E-Institutes of Shanghai Municipal Education Commission （Crant No. E03004） and the Natural Science Foundation of Zhejiang Province of China （Grant No. Y6090164）.
文摘A class of generalized complex Burgers equation is considered. First, a set of equations of the complex value functions are solved by using the homotopic mapping method. The approximate solution for the original generalized complex Burgers equation is obtained. This method can find the approximation of arbitrary order of precision simply and reliably.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 90111011 and 10471039）, the State Key Development Program for Basic Research of China （Grant Nos 2003CB415101-03 and 2004CB418304）, the Key Project of the Chinese Academy of Sciences （Grant No KZCX3-SW-221）, in part by E-Institutes of Shanghai Municipal Education Commission （Grant No N.E03004）, and the Natural Science Foundation of Zhejiang Province, China （Grant No Y604127）.
文摘The E1 Nifio/La Nifia Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. In this paper, a coupled system of sea-air oscillator model is studied. The aim is to create an asymptotic solving method of nonlinear equation for the ENSO model. And based on a class of oscillators of ENSO model, employing the method of homotopic mapping, the approximate solution of corresponding problem is studied. It is proven from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere-ocean oscillation for ENSO model.
基金Project supported by the National Natural Science Foundation of China (Grant No. 40876010)the Knowledge Innovation Project of Chinese Academy of Sciences (Grant No. KZCX2-YW-Q03-08)+1 种基金LASG State Key Laboratory Special Fund,E-Institutes of Shanghai Municipal Education Commission (Grant No. E03004)the Natural Science Foundation of Zhejiang Province,China(Grant No. Y6090L4)
文摘A reduces equation of the Kelvin wave is considered. By using the homotopic mapping solving method, the approximate solution is obtained. The homptopic mapping method is an analytic method, the obtained solution can analyse operations sequentially.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 40676016 and 40876010)the State Key Development Program for Basic Research of China (Grant Nos 2003CB415101-03 and 2004CB418304)+1 种基金the Key Innovation Project of Chinese Academy of Sciences (Grant No KZCX2-YW-Q03-08)the LASG State Key Laboratory Special Fund and in part by E-Institutes of Shanghai Municipal Education Commission (Grant No E03004)
文摘This paper considers a class of oscillator for the El Nino/La Ninia-southern oscillation （ENSO） model. By using the homotopic mapping method, it obtains approximations of the solution for the ENSO model.
基金Project supported by the National Natural Science Foundation of China(Grant Nos40679016 and 10471039)the State Key Program for Basic Research of China(Grant Nos2003CB415101-03 and 2004CB418304)+2 种基金the Key Basic Research Foundation ofthe Chinese Academy of Sciences,China(Grant No KZCX3-SW-221)partially by E-Institutes of Shanghai Municipal Education Commission of China(Grant No N.E03004)the Natural Science Foundation of Zhejiang Province,China(Grant No Y60628)
文摘The EI Nimo and Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific sea-air interactions. In this paper, an asymptotic method of solving nonlinear equations for the ENSO model is proposed. And based on a class of oscillator of the ENSO model and by employing the method of homotopic mapping, the approximate solution of equations for the corresponding ENSO model is studied. It is proved from the results that homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial Pacific of the sea-air oscillator for the ENSO model.
基金Under the auspices of National Natural Science Foundation of China(No.40876010)Main Direction Program of Knowledge Innovation Programs of the Chinese Academy of Sciences(No.KZCX2-YW-Q03-08)+3 种基金R & D Special Fund for Public Welfare Industry(meteorology)(No.GYHY200806010)LASG State Key Laboratory Special FundFoundation of Shanghai Municipal Education Commission(No.E03004)Natural Science Foundation of Zhejiang Province(No.Y6090164)
文摘The thermally and wind-driven ocean circulation is a complicated natural phenomenon in the atmospheric physics. Hence we need to reduce it using basic models and solve the models using approximate methods. A non-linear model of the thermally and wind-driven ocean circulation is used in this paper. The results show that the zero solution of the linear equation is a stable focus point, which is the path curve trend origin point as time (t) trend to infinity. By using the homotopic mapping perturbation method, the exact solution of the model is obtained. The homotopic mapping perturbation method is an analytic solving method, so the obtained solution can be used for analytic operating sequentially. And then we can also obtain the diversified qualitative and quantitative behaviors for corresponding physical quantities.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 40676016 and 40876010)the Key Innovation Project of the Chinese Academy of Sciences (Grant No KZCX2-YW-Q03-08)LASG State Key Laboratory Special Fund, China, and in part by E-Institutes of Shanghai Municipal Education Commission, China (Grant No E03004)
文摘A class of generalized Vakhnemko equation is considered. First, we solve the nonlinear differential equation by the homotopic mapping method. Then, an approximate soliton solution for the original generalized Vakhnemko equation is obtained. By this method an arbitrary order approximation can be easily obtained and, similarly, approximate soliton solutions of other nonlinear equations can be acquired.
