Dynamics of Partial Differential Equations

Volume 19 (2022)

Number 2

Traveling waves of a generalized nonlinear Beam equation

Pages: 91 – 121

DOI: https://dx.doi.org/10.4310/DPDE.2022.v19.n2.a1

Authors

Amin Esfahani (Department of Mathematics, Nazarbayev University, Nur-Sultan, Kazakhstan)

Steven Levandosky (Department of Mathematics and Computer Science, College of the Holy Cross, Worcester, Massachusetts, U.S.A.)

Abstract

We consider the existence and stability of traveling waves of a nonlinear beam equation for a general class of non-homogeneous nonlinearities. We use variational methods to prove existence of ground state traveling wave solutions for this class and analyze their stability. We also present a numerical method based on the variational characterization of ground states and use it to determine intervals of wave speeds for which ground states are stable.

Keywords

nonlinear beam equation, traveling wave, stability, variational methods

2010 Mathematics Subject Classification

35B35, 35B40, 35J35, 35L75, 35Qxx

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Received 8 September 2021

Published 19 May 2022