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Reduction of soliton equations in bilinear form. (English) Zbl 0601.35099
The author generalizes the studies of the Kyoto group (M. Sato, Y. Sato, E. Date, M. Kashivara, M. Jimbo, T. Miva) on the reduction of the Kadomtsev-Petviashvili equation (KP) to the Korteweg de Vries equation (KdV), the Boussinesq equation and on some other reductions. The paper introduces a so called ”n-pseudo reduction” method and a special reduction \((pq=c)\) which being applied to the KP hierarchy generates the classical Boussinesq equation and nonlinear Schrödinger equation exhibiting Dark-soliton solutions. A reduction of the Boussinesq-KP equation generates the \(''KdV+Sawada\)-Kotera” equation which exhibits resonances of solitons.
Reviewer: J.Kostarčuk

MSC:
35Q99 Partial differential equations of mathematical physics and other areas of application
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