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

Marcos Caso Huerta*, Antonio Degasperis, Sara Lombardo, Matteo Sommacal

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)
14 Downloads (Pure)


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.
Original languageEnglish
Article number20210408
Pages (from-to)1-18
Number of pages18
JournalProceedings of the Royal Society A
Issue number2252
Early online date18 Aug 2021
Publication statusPublished - 25 Aug 2021


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