Genuine nonlinearity and its connection to the modified Korteweg–de Vries equation in phase dynamics

Ratliff, Daniel (2022) Genuine nonlinearity and its connection to the modified Korteweg–de Vries equation in phase dynamics. Nonlinearity, 35 (1). pp. 30-65. ISSN 0951-7715

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The study of hyperbolic waves involves various notions which help characterise how these structures evolve. One important facet is the notion of genuine nonlinearity, namely the ability for shocks and rarefactions to form instead of contact discontinuities. In the context of the Whitham modulation equations, this paper demonstrate that a loss of genuine nonlinearity leads to the appearance of a dispersive set of dynamics in the form of the modified Korteweg de-Vries equation governing the evolution of the waves instead. Its form is universal in the sense that its coefficients can be written entirely using linear properties of the underlying waves such as the conservation laws and linear dispersion relation. This insight is applied to two systems of physical interest, one an optical model and the other a stratified hydrodynamics experiment, to demonstrate how it can be used to provide insight into how waves in these systems evolve when genuine nonlinearity is lost.

Item Type: Article
Uncontrolled Keywords: Lagrangian dynamics, modulation, internal waves, optics, nonlinear waves, hyperbolic systems
Subjects: F300 Physics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Rachel Branson
Date Deposited: 10 Dec 2021 16:28
Last Modified: 10 Dec 2021 16:30

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