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Published April 1991 | public
Journal Article

Commutation methods applied to the mKdV-equation

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.

Additional Information

© 1991 American Mathematical Society. Dedicated to Raphael Heegh-Krohn (1938-1988). Received by the editors January 15, 1990. The first author is a Max Kade Foundation Fellow and, with the third author, was partially supported by USNSF under Grant DMS-8801918. The second author was supported by BMFT, Federal Republic of Germany. We are indebted to David Gurarie for several most stimulating discussions. F. Gesztesy is indebted to D. Wales for the hospitality extended to him at Caltech. He also gratefully acknowledges financial support from the Max Kade Foundation and from USNSF under Grant DMS-8801918.

Additional details

Created:
August 19, 2023
Modified:
October 25, 2023