A new integrable model of long wave–short wave interaction and linear stability spectra

Caso Huerta, Marcos, Degasperis, Antonio, Lombardo, Sara and Sommacal, Matteo (2021) A new integrable model of long wave–short wave interaction and linear stability spectra. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477 (2252). p. 20210408. ISSN 1364-5021

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Official URL: https://doi.org/10.1098/rspa.2021.0408


We consider the propagation of short waves which generate waves of much longer (infinite) wavelength. Model equations of such long wave–short wave (LS) resonant interaction, including integrable ones, are well known and have received much attention because of their appearance in various physical contexts, particularly fluid dynamics and plasma physics. Here we introduce a new LS integrable model which generalizes those first proposed by Yajima and Oikawa and by Newell. By means of its associated Lax pair, we carry out the linear stability analysis of its continuous wave solutions by introducing the stability spectrum as an algebraic curve in the complex plane. This is done starting from the construction of the eigenfunctions of the linearized LS model equations. The geometrical features of this spectrum are related to the stability/instability properties of the solution under scrutiny. Stability spectra for the plane wave solutions are fully classified in the parameter space together with types of modulational instabilities.

Item Type: Article
Additional Information: Funding information: This research was partially funded by a London Mathematical Society Research in Pairs grant (no. 41808).
Uncontrolled Keywords: nonlinear waves, integrable systems, wave coupling, long wave–short wave resonant interaction, linear stability of plane waves
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Elena Carlaw
Date Deposited: 19 Aug 2021 09:04
Last Modified: 02 Sep 2021 15:15
URI: http://nrl.northumbria.ac.uk/id/eprint/46943

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