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The "direct method" proposed by R. Hirota in 1971 is a very effective tool for constructing soliton solutions and has been applied to almost all integrable equations. In applying this method the condi...tion of integrability appears when one tries to construct three-soliton solutions, whereas two-soliton solutions can be constructed even for non-integrable equations. Here we apply this method to fully discrete lattice equations defined on a 2 × N stencil. It turns out that all the results obtained can also be obtained by reductions from the Hirota-Miwa equation. Thus the three-soliton condition is again found to give same results as other integrability criteria.show more
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Article_No_05