We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations toCauchy problems for systems of ordinary differential equations (ODEs).We classify a class of fourth-order evoluti...We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations toCauchy problems for systems of ordinary differential equations (ODEs).We classify a class of fourth-order evolutionequations which admit certain higher-order generalized conditional symmetries (GCSs) and give some examples to showthe main reduction procedure.These reductions cannot be derived within the framework of the standard Lie approach,which hints that the technique presented here is something essential for the dimensional reduction of evolu tion equations.展开更多
As an approach to the technological problem that the wind data of QuikSCAT scatterometer cannot accurately describe the zone of typhoon-level strong wind speed, some objective factors such as the typhoon moving speed,...As an approach to the technological problem that the wind data of QuikSCAT scatterometer cannot accurately describe the zone of typhoon-level strong wind speed, some objective factors such as the typhoon moving speed, direction and friction are introduced in this study to construct the asymmetric strengthening of the QuikSCAT wind field. Then by adopting a technology of four-dimensional data assimilation, an experiment that includes both the assimilation and forecasting phases is designed to simulate Typhoon Rananim numerically. The results show that with model constraints and adjustment, this technology can incorporate the QuikSCAT wind data to the entire column of the model atmosphere, improve greatly the simulating effects of the whole-column wind, pressure field and the track as well as the simulated typhoon intensity covered by the forecast phase, and work positively for the forecasting of landfall locations.展开更多
基金National Natural Science Foundation of China under Grant Nos.10447007 and 10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.2005A13
文摘We exploit higher-order conditional symmetry to reduce initial-value problems for evolution equations toCauchy problems for systems of ordinary differential equations (ODEs).We classify a class of fourth-order evolutionequations which admit certain higher-order generalized conditional symmetries (GCSs) and give some examples to showthe main reduction procedure.These reductions cannot be derived within the framework of the standard Lie approach,which hints that the technique presented here is something essential for the dimensional reduction of evolu tion equations.
基金National Key Fundamental Research and Development Plan of China (2004CB418301)Natural Science Foundation of China (40830958)
文摘As an approach to the technological problem that the wind data of QuikSCAT scatterometer cannot accurately describe the zone of typhoon-level strong wind speed, some objective factors such as the typhoon moving speed, direction and friction are introduced in this study to construct the asymmetric strengthening of the QuikSCAT wind field. Then by adopting a technology of four-dimensional data assimilation, an experiment that includes both the assimilation and forecasting phases is designed to simulate Typhoon Rananim numerically. The results show that with model constraints and adjustment, this technology can incorporate the QuikSCAT wind data to the entire column of the model atmosphere, improve greatly the simulating effects of the whole-column wind, pressure field and the track as well as the simulated typhoon intensity covered by the forecast phase, and work positively for the forecasting of landfall locations.
