The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical system...The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.展开更多
Large amplitude internal solitary waves(ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean.We observed highly nonlinear ISWs over the continent...Large amplitude internal solitary waves(ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean.We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea(19°35'N,112°E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors,and an acoustic Doppler current profiler(ADCP).We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories.Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width.Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries(KdV) theory than the first-order KdV model.These results indicate that the northwestern South China Sea(SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.展开更多
Both large amplitude depression and elevation internal solitary waves （ISWs） were observed on the continental shelf of the northwest South China Sea （SCS） during the Wenchang Intemal Wave Experiment. In this study...Both large amplitude depression and elevation internal solitary waves （ISWs） were observed on the continental shelf of the northwest South China Sea （SCS） during the Wenchang Intemal Wave Experiment. In this study, we investigate the characteristics of depression and elevation ISWs based on comparisons between observational results and internal wave theories. It is suggested that the large amplitude depression wave is better represented by the extended Korteweg-de Vries （EKdV） theory than by the KdV model, whereas the large amplitude elevation wave is in better agreement with the KdV equation than with the EKdV theory. Wave-induced forces on a supposed small-diameter cylindrical pile by depression and elevation waves are also estimated using the internal wave theory and Morison formula. The wave-induced force by elevation ISWs is rarely reported in the literature. It is found that the force induced by the elevation wave differs significantly fi＇om that by the depression wave, and the elevation wave generally produces greater force on the pile in the lower water column than the depression wave. These results show that ISWs in the study area can present a serious threat to ocean engineering structures, and should not be ignored in the design of oil platforms and ocean operations.展开更多
基金National Natural Science Foundation of China(No.19731003,No.19961003)Yunnan Provincial Natural Science Foundation of China(No.1999A0018M,No.2000A0002M)
文摘The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.
基金Supported by the Knowledge Innovation Program of Chinese Academy of Sciences (No.KZCX1-YW-12)the National High Technology Research and Development Program of China (863 program) (No.2008AA09A401,No.2006AA09A109)
文摘Large amplitude internal solitary waves(ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean.We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea(19°35'N,112°E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors,and an acoustic Doppler current profiler(ADCP).We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories.Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width.Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries(KdV) theory than the first-order KdV model.These results indicate that the northwestern South China Sea(SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.
基金Supported by the National Natural Science Foundation of China(Nos.41106017,41030855)the Knowledge Innovation Program of Chinese Academy of Sciences(No.KZCX1-YW-12)+1 种基金the Natural Science Foundation of Jiangsu Province of China(No.BK2011396)the National High Technology Research and Development Program of China(863program)(No.2008AA09A401)
文摘Both large amplitude depression and elevation internal solitary waves （ISWs） were observed on the continental shelf of the northwest South China Sea （SCS） during the Wenchang Intemal Wave Experiment. In this study, we investigate the characteristics of depression and elevation ISWs based on comparisons between observational results and internal wave theories. It is suggested that the large amplitude depression wave is better represented by the extended Korteweg-de Vries （EKdV） theory than by the KdV model, whereas the large amplitude elevation wave is in better agreement with the KdV equation than with the EKdV theory. Wave-induced forces on a supposed small-diameter cylindrical pile by depression and elevation waves are also estimated using the internal wave theory and Morison formula. The wave-induced force by elevation ISWs is rarely reported in the literature. It is found that the force induced by the elevation wave differs significantly fi＇om that by the depression wave, and the elevation wave generally produces greater force on the pile in the lower water column than the depression wave. These results show that ISWs in the study area can present a serious threat to ocean engineering structures, and should not be ignored in the design of oil platforms and ocean operations.
