Differential and Integral Equations

On the (modified) Kadomtsev-Petviashvili hierarchy

F. Gesztesy and K. Unterkofler

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Abstract

We present a novel approach to the Kadomtsev-Petviashvili (KP) hierarchy and its modified counterpart, the mKP hierarchy based on factorizations of formal pseudo-differential operators and a matrix-valued Lax operator for the mKP hierarchy. As a result of this framework we obtain new B\"acklund transformations for the KP hierarchy and the possibility of transferring classes of KP solutions into those of mKP solutions, and vice versa. As an application of our techniques we provide a new derivation of soliton solutions of the KP and mKP equation.

Article information

Source
Differential Integral Equations, Volume 8, Number 4 (1995), 797-812.

Dates
First available in Project Euclid: 20 May 2013

Permanent link to this document
https://projecteuclid.org/euclid.die/1369055611

Mathematical Reviews number (MathSciNet)
MR1306592

Zentralblatt MATH identifier
0830.35117

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

Citation

Gesztesy, F.; Unterkofler, K. On the (modified) Kadomtsev-Petviashvili hierarchy. Differential Integral Equations 8 (1995), no. 4, 797--812. https://projecteuclid.org/euclid.die/1369055611


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