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Lump Solutions for PDE’s: Algorithmic Construction and Classification

Abstract In this paper we apply truncated Painlevé expansions to the Lax pair of a PDE to derive gauge-Bäcklund transformations of this equation. It allows us to construct an algorithmic method to derive solutions by starting from the simplest one. Actually, we use this method to obtain an infinite set of lump solutions that can be classified by means of two integer numbers N and M. Two different PDE’s are used to check the method and compare the results.