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Continuity of the Scattering Transformation for the Korteweg de Vries Equation

Published online by Cambridge University Press:  20 November 2018

Henri-François Gautrin  and
Tapio Klemola
Henri-François Gautrin
Affiliation:
University of Montreal, Montreal, Quebec
Tapio Klemola
Affiliation:
University of Montreal, Montreal, Quebec
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It is at present well known that, if q(x, t) is a solution of the Korteweg de Vries (K d V) equation

(1)

such that q(x, 0) = q0(x), where q0(x) behaves reasonably at infinity, and if

are the scattering data (see [4]) corresponding to q(x, t), then

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 2 , 01 April 1986 , pp. 360 - 375
Copyright
Copyright © Canadian Mathematical Society 1986

References

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4. Faddeev, L. D., Properties of the S-matrix of the one-dimensional Schroëdinger equation, Trusdy, mat. inst., Steklov 73 (1964), 314.Google Scholar
5. Montel, P., Leçons sur les familles normales de fonctions analytiques et leurs applications (Chelsea publishing company, New York, 1974).Google Scholar
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