Abstract
Recently, in the Fermi-Pasta-Ulam chain stable self-localized solitons (SLS) have been found. In the present investigation a construction procedure for SLS solutions is presented. It is based on two ingredients: (a) the exploitation of the harmonic wing property and (b) a Gaussian step-by-step optimization starting from the wing. The procedure allows for highly accurate approximate solutions. The temporal stability of the solutions is verified.
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