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arXiv · 2501.07940

Notes on number of one-troughed travelling waves in asymmetrically supported bending beam

Hana Formánková Levá·Gabriela Holubová
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Abstract

We study the boundary value problem for nonlinear fourth-order partial differential equation with jumping nonlinearity which can serve, e.g., as a model of an asymmetrically supported bending beam. We focus on a special type of solutions, the so-called one-troughed travelling waves. The main goal of this paper is to show the existence of at least two different one-troughed travelling waves for particular wave speeds and input parameters of the studied problem. We present the upper bounds for the maximal number of one-troughed solutions together with a visualisation of obtained results and corresponding solutions. Finally, we list several open questions regarding this topic.

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Hana Formánková Levá, Gabriela Holubová. 2025-01-14. Notes on number of one-troughed travelling waves in asymmetrically supported bending beam. https://doi.org/10.21136/am.2025.0035-25

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