中国数学科学.ppt

2006 中国数学科学与教育发展论坛;Capillary waves;Gravity waves;Water waves of depth h;Key parameters of water waves;Dispersion relations on linear theory;Water particle pathlines in waters;Wave packet dispersion;Wave packet group dispersion;Generation of ship waves;;Ship wave in shallower waters;Ship wave pattern;;John Scott Russell’s 1834 chance discovery;;Significances of the KdV evolution equation;Grand discovery of the remarkable soliton ;Remarkable properties of solitons;Forced forward-radiation of solitons;Exciting discovery of forward-radiating solitons at Wu’s Laboratory - 1982;Agreement between theory and experiment;Comparison between experiment and theory;Experimental and computational views of forced radiation of solitary waves;Hydrodynamic instabilities of resonantly forced solitons;Part IReflection for Insight on Solitary Waves of Arbitrary Height;Sir G.G.Stokes (1880) on the solitary wave outskirts;Reflective Queries;F2 = 1.15 ?=0.196541;Reflections on ;Sir G. G. Stokes (1880):  Corner wedge flow under gravity;Formulation and analysis;Unified intrinsic functional expansion (UIFE) theory;The highest solitary wave;A dwarf solitary wave -- with F =1.005 (m = 0.054873);Reflections on ;Variations of ?(?) and F(?) – by UIFE – I-II;Graphical presentation of numerical solutions;Sample profiles of extreme solitary waves;Wave profiles evaluated by UIFE-I and II;Integral properties of solitary waves;Comparison with three lower-order theories;Unified Perturbation Expansion For Solitary Waves;Motivated reflection and queries;Literature contributions;Guiding principles;A unified perturbation expansion theory;Asymptotic reductive perturbation scheme;Exact higher-order theory of O( ?18 );Exact theory of O( ?18 );;;;;;On solitary waves - part 3, Wang, X.L. and Wu, T.Y. Physics Letters A 350 (2006), 44-50;Wave Elevation and Amplitude: Divergent Solutions;Amplitude vs. ?=k2h2;Integral convergence;Integral convergence (cont.);Domb-Sykes Plot;Near-source devastation of t