Stability and Instability of Solitary Waves of Korteweg-de Vries Type

作者: Jerry L Bona , Panagiotis E Souganidis , Walter A Strauss

DOI: 10.1098/RSPA.1987.0073

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摘要: … Special cases for which our analysis is decisive include equations of the Korteweg-de Vries … the equation for surface water waves in a canal, derived by Korteweg & deVries (1895). For …

参考文章(11)
J.P. Albert, J.L. Bona, D.B. Henry, Sufficient conditions for stability of solitary-wave solutions of model equations for long waves Physica D: Nonlinear Phenomena. ,vol. 24, pp. 343- 366 ,(1987) , 10.1016/0167-2789(87)90084-4
Jerry L. Bona, Vassilios A. Dougalis, Ohannes A. Karakashian, Fully discrete galerkin methods for the korteweg-de vries equation☆ Computers & Mathematics With Applications. ,vol. 12, pp. 859- 884 ,(1986) , 10.1016/0898-1221(86)90031-3
D. J. Korteweg, G. de Vries, XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves Philosophical Magazine Series 1. ,vol. 39, pp. 422- 443 ,(1895) , 10.1080/14786449508620739
Manoussos Grillakis, Jalal Shatah, Walter Strauss, Stability theory of solitary waves in the presence of symmetry, II☆ Journal of Functional Analysis. ,vol. 94, pp. 308- 348 ,(1990) , 10.1016/0022-1236(90)90016-E
W. Eckhaus, P. Schuur, The emergence of solitons of the korteweg‐de vries equation from arbitrary initial conditions Mathematical Methods in The Applied Sciences. ,vol. 5, pp. 97- 116 ,(1983) , 10.1002/MMA.1670050108
Clifford S. Gardner, John M. Greene, Martin D. Kruskal, Robert M. Miura, Method for solving the Korteweg-deVries equation Physical Review Letters. ,vol. 19, pp. 1095- 1097 ,(1967) , 10.1103/PHYSREVLETT.19.1095
A Numerical and Theoretical Study of Certain Nonlinear Wave Phenomena Philosophical transactions - Royal Society. Mathematical, physical and engineering sciences. ,vol. 289, pp. 373- 404 ,(1978) , 10.1098/RSTA.1978.0064
G Scharf, W.F Wreszinski, Stability for the Korteweg-de Vries equation by inverse scattering theory Annals of Physics. ,vol. 134, pp. 56- 75 ,(1981) , 10.1016/0003-4916(81)90004-X
T. Brooke Benjamin, Internal waves of permanent form in fluids of great depth Journal of Fluid Mechanics. ,vol. 29, pp. 559- 592 ,(1967) , 10.1017/S002211206700103X
On the stability theory of solitary waves Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 344, pp. 363- 374 ,(1975) , 10.1098/RSPA.1975.0106