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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)



New types of soliton solutions

Authors: F. Gesztesy, W. Karwowski and 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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