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Prog. Theor. Phys. Vol. 76 No. 4 (1986) pp. 768-783
Fredholm Determinant and the Solution of the Korteweg-de Vries Equation
Yusuke Kato
Department of Engineering Mathematics, Utsunomiya University, Utsunomiya, Tochigi 321
(Received June 2, 1986)
Abstract:
The Marchenko integral equation for the Schrödinger equation on the whole line is analysed in the framework of the Fredholm theory and its solution, the Schrödinger potential, is given in terms of the Fredholm determinant. The evolution of the potential due to the evolution of the scattering data is proved to produce the solution of the Cauchy problem of the Korteweg-de Vries equation for smooth, rapidly decreasing initial value. A similarity law of the solution is presented.
URL :
http://ptp.ipap.jp/link?PTP/76/768/
DOI : 10.1143/PTP.76.768
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Citing Article(s) :
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Progress of Theoretical Physics Vol. 78 No. 2 (1987) pp. 198-213
:
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Fredholm Determinants and the Cauchy Problem of a Class of Nonlinear Evolution Equations
-
Yusuke Kato
-
Progress of Theoretical Physics Vol. 83 No. 6 (1990) pp. 1090-1107
:
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Fredholm Determinant Solution for the Inverse Scattering Transform of the N ×N Zakharov-Shabat Equation
-
Naruyoshi Asano and Yusuke Kato
