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Existence of solitons in the nonlinear beam equation

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Abstract

This paper concerns the existence of solitons, namely stable solitary waves in the nonlinear beam equation with a suitable nonlinearity. An equation of this type has been introduced in [P. J. McKenna and W. Walter, Arch. Ration. Mech. Anal., 98 (1987), 167-177] as a model of a suspension bridge. We prove both the existence of solitary waves for a large class of nonlinearities and their stability. As far as we know this is the first result about stability of solitary waves in nonlinear beam equation.

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Authors and Affiliations

  1. Dipartimento di Matematica Applicata “U. Dini”, Università degli Studi di Pisa, Via Filippo Buonarroti 1/c, 56127, Pisa, Italy

    Vieri Benci

  2. College of Science, Department of Mathematics, King Saud University, Riyadh, 11451, Saudi Arabia

    Vieri Benci

  3. Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, Via Orabona 4, 70125, Bari, Italy

    Donato Fortunato

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  1. Vieri Benci
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  2. Donato Fortunato
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Correspondence to Vieri Benci.

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To Dick Palais on the occasion of his 80th birthday

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Benci, V., Fortunato, D. Existence of solitons in the nonlinear beam equation. J. Fixed Point Theory Appl. 11, 261–278 (2012). https://doi.org/10.1007/s11784-012-0080-5

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  • DOI: https://doi.org/10.1007/s11784-012-0080-5

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