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September 18, 2025Open Access

Soliton-like solutions for a nonlinear doubly dispersive equation in an elastic Murnaghan's rod via Hirota's bilinear method

Key Points

Various solitary wave solutions were derived using Hirota's bilinear method, enhancing understanding of chaotic dynamics.
The study reveals multiple waves and dark solitons through numerical simulations using Mathematica software for graphical depiction.
Hirota's bilinear transformation was employed in this nonlinear framework to explore wave behaviors in the elastic Murnaghan's rod.
The findings support further exploration of chaotic wave movement in elastic materials under governed nonlinear equations.

Abstract

Abstract The purpose of this work is to study the physical phenomena of the doubly dispersive model that controls chaotic wave movement in the elastic Murnaghan’s rod. The method of Hirota bilinear transformation is employed to derive various forms of solitary wave solutions, such as multiple waves, periodic lump waves, periodic cross-kink waves, homoclinic breather waves, dark soliton, and mixed waves. In order to see their physical behavior, we use the Mathematica software with selected values of the model parameters to depict their graphical behavior.

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