New types of soliton solutions
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- by F. Gesztesy, W. Karwowski and Z. Zhao PDF
- Bull. Amer. Math. Soc. 27 (1992), 266-272 Request permission
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.References
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Additional Information
- © Copyright 1992 American Mathematical Society
- 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