A Method of Analysing Soliton Equations by Bilinearization

Shin'ichi Oishi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


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
Issue number2
Publication statusPublished - 1980

ASJC Scopus subject areas

  • General Physics and Astronomy


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