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New types of soliton solutions
Author(s):
F.
Gesztesy;
W.
Karwowski;
Z.
Zhao
Journal:
Bull. Amer. Math. Soc.
27
(1992),
266-272.
MSC (2000):
Primary 35Q51;
Secondary 35Q53
MathSciNet review:
1152159
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Abstract:
We announce a detailed investigation of limits of N-soliton solutions of the Korteweg-deVries (KdV) equation as N tends to infinity. Our main results provide new classes of KdV-solutions including in particular new types of soliton-like (reflectionless) solutions. As a byproduct we solve an inverse spectral problem for one-dimensional Schrödinger operators and explicitly construct smooth and real-valued potentials that yield a purely absolutely continuous spectrum on the nonnegative real axis and give rise to an eigenvalue spectrum that includes any prescribed countable and bounded subset of the negative real axis.
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Additional Information:
DOI:
10.1090/S0273-0979-1992-00309-9
PII:
S 0273-0979(1992)00309-9
Copyright of article:
Copyright
1992,
American Mathematical Society
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