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

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.

💡 Research Summary

The paper investigates a fourth‑order nonlinear partial differential equation (PDE) that models an asymmetrically supported bending beam. The governing equation is

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