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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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