Orbital stability investigations for travelling waves in a nonlinearly supported beam

[摘要] We consider the fourth-order wave equation phi(tt) + phi(xxxx) + f(phi) = 0, (x, t) is an element of R x R, with a nonlinearity f vanishing at 0. Travelling waves phi(x, t) = u(x - ct) satisfy the ODE u' + c(2)u '' + f(u) = 0 on R, and for the case f (u) = e(u) - 1, the existence of at least 36 solitary travelling waves was proved in [4] by computer assisted means. We investigate the orbital stability of these solutions via computation of their Morse indices and using results from [11] and [12]. In order to achieve our results we make use of both analytical and computer-assisted techniques. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-15

[关键词] Orbital stability;Travelling wave;Computer-assisted proof