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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Commutation methods applied to the mKdV-equation


Authors: F. Gesztesy, W. Schweiger and B. Simon
Journal: Trans. Amer. Math. Soc. 324 (1991), 465-525
MSC: Primary 35Q53; Secondary 34L25, 47E05, 58F07
MathSciNet review: 1029000
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Abstract: An explicit construction of solutions of the modified Korteweg-de Vries equation given a solution of the (ordinary) Korteweg-de Vries equation is provided. Our theory is based on commutation methods (i.e., $ N = 1$ supersymmetry) underlying Miura's transformation that links solutions of the two evolution equations.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1029000-7
PII: S 0002-9947(1991)1029000-7
Keywords: $ \operatorname{mKdV} $-equation, commutation methods, soliton-like solutions, periodic solutions, singular solutions
Article copyright: © Copyright 1991 American Mathematical Society