A Method of Analysing Soliton Equations by Bilinearization

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Abstract

Recently, a class of new solutions have been derived for a number of soliton equations using Hirota's bilinear forms of these soliton equations (S. Oishi: J. Phys. Soc. Jpn. 47 (1979) 1341). These solutions express solitons in a background of ripples, and are named generalized soliton solutions. In this paper, it is shown that the generalized soliton solutions for the Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation can be transformed into a form of Fredholm's determinants of the Gel'fand-Levitan-Marchenko integral equation. Using this result, relationship between Hirota's method and the inverse spectral method is clarified. Moreover, it is also shown that the initial value problems for these two equations can be solved using their generalized soliton solutions.

Original languageEnglish
Pages (from-to)639-646
Number of pages8
Journaljournal of the physical society of japan
Volume48
Issue number2
DOIs
Publication statusPublished - 1980 Jan 1

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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