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

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journal contribution
posted on 12.10.2021, 14:10 by Marcos Caso-Huerta, Antonio Degasperis, Sara LombardoSara Lombardo, Matteo Sommacal
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.

Funding

London Mathematical Society Research in Pairs grant (no. 41808)

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volume

477

Issue

2252

Publisher

The Royal Society

Version

VoR (Version of Record)

Rights holder

© The authors

Publisher statement

This is an Open Access Article. It is published by The Royal Society under the Creative Commons Attribution 4.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/4.0/

Acceptance date

19/07/2021

Publication date

2021-08-18

Copyright date

2021

ISSN

1364-5021

eISSN

1471-2946

Language

en

Depositor

Deposit date: 12 October 2021

Article number

20210408