Modulations of KdV wavetrains. (English) Zbl 1194.35377

Summary: This lecture summarizes some work on the modulational theory of Korteweg de Vries wave trains which was done by H. Flaschka, G. Forest and D.W. McLaughlin during the past year [cf. Commun. Pure Appl. Math. 33, 739–784 (1980; Zbl 0454.35080)].


35Q53 KdV equations (Korteweg-de Vries equations)


Zbl 0454.35080
Full Text: DOI


[1] Dubrovin, B.A.; Matveev, V.B.; Novikov, S.P., Nonlinear equations of Korteweg de Vries type, finite zoned linear operators, and abelian varieties, Uspekhi mat. nauk, 31, 55-136, (1976) · Zbl 0326.35011
[2] McKean, H.P.; van Moerbeke, P., The spectrum of Hill’s equation, Inventions math., 30, 271-274, (1975) · Zbl 0319.34024
[3] Whitham, G.B., Linear and nonlinear waves, (1974), Wiley-Interscience New York · Zbl 0373.76001
[4] Whitham, G.B., Non-linear dispersive waves, (), 238-261 · Zbl 0125.44202
[5] Miura, R.; Krustal, M., Application of a nonlinear WKB method to the Korteweg de Vries equation, SIAM J. appl. math., 26, 376-395, (1974) · Zbl 0273.35055
[6] Flaschka, H.; Forest, G.; McLaughlin, D.W., Multiphase averaging and the inverse spectral solution on K.d.V., Comm. pure appl. math., (1980), to appear · Zbl 0454.35080
[7] Forest, G.; McLaughlin, D.W., Canonical variables for periodic sine-Gordon equation and a method of averaging, LA-UR 78-3318, report of los alamos scientific laboratory, (1978)
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