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Title Hirota's direct method and the three-soliton condition

Name Jarmo Hietarinta
Country Finland
Email hietarin@utu.fi
Co-Author(s) Da-jun Zhang
Submit Time 2010-02-12 08:47:16
Special Session 66: Discrete Integrable Systems
Integrable PDEs are characterized by many interesting properties, one of which is the existence of multi-soliton solutions. The construction of these solutions is particularly simple using Hirota's direct method. It turns out that although many equations have one and even two-soliton solutions, the existence of three-soliton solutions is in practice equivalent to integrability. This provides a method for searching for integrable equations. We briefly review the situation in the continuum case and present some new results in the discrete case.