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

DOI:
https://doi.org/10.1090/S0273-0979-1992-00309-9

MathSciNet review:
1152159

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0273-0979-1992-00309-9

Article copyright:
© Copyright 1992
American Mathematical Society