New types of soliton solutions
Authors:
F. Gesztesy, W. Karwowski and Z. Zhao
Journal:
Bull. Amer. Math. Soc. 27 (1992), 266272
MSC (2000):
Primary 35Q51; Secondary 35Q53
MathSciNet review:
1152159
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Abstract: We announce a detailed investigation of limits of Nsoliton solutions of the KortewegdeVries (KdV) equation as N tends to infinity. Our main results provide new classes of KdVsolutions including in particular new types of solitonlike (reflectionless) solutions. As a byproduct we solve an inverse spectral problem for onedimensional Schrödinger operators and explicitly construct smooth and realvalued 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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 P. A. Deift, Applications of a commutation formula, Duke Math. J. 45 (1978), 267310. MR 495676 (81g:47001)
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 H. Grosse, Quasiclassical estimates on moments of the energy levels, Acta Phys. Austriaca 52 (1980), 89105. MR 584458 (82g:81017)
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 F. Mantlik and A. Schneider, Note on the absolutely continuous spectrum of SturmLiouville operators, Math. Z. 205 (1990), 491498. MR 1082870 (92b:34103)
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 U.W. Schmincke, On Schrödinger's factorization method for SturmLiouville operators, Proc. Roy. Soc. Edinburgh Sect. A 80 (1978), 6784. MR 529570 (80f:34025)
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 V. E. Zakharov and L. D. Faddeev, Kortewegde Vries equation: A completely integrable Hamiltonian system, Funct. Anal. Appl. 5 (1971), 280287.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S027309791992003099
PII:
S 02730979(1992)003099
Article copyright:
© Copyright 1992
American Mathematical Society
