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Recently, stable self-localized solitons (SLS) have been found in the Fermi-Pasta-Ulam (FPU) chain. 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, which already surpass in the one-frequency version the accuracy of previous solutions. The method is illustrated for the quartic FPU chain, but it is not restricted to this type of anharmonicity.
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Dusi et al. (1995) studied this question.
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