Existence of solitons in the nonlinear beam equation

TL;DR

This paper proves the existence and stability of solitons in the nonlinear beam equation, a model for suspension bridges, marking the first stability result for such solitary waves.

Contribution

It establishes the existence and stability of solitary waves in the nonlinear beam equation, a novel result in this area.

Findings

Existence of solitary waves for a broad class of nonlinearities.

First proof of stability of solitary waves in the nonlinear beam equation.

Abstract

This paper concerns with the existence of solitons, namely stable solitary waves in the nonlinear beam equation (NBE) with a suitable nonlinearity. An equation of this type has been introduced by P.J. McKenna and W. Walter 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 NBE.