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Nonlinear Sciences > Exactly Solvable and Integrable Systems

arXiv:2109.04296 (nlin)
[Submitted on 9 Sep 2021]

Title:A new integrable model of long wave-short wave interaction and linear stability spectra

Authors:Marcos Caso-Huerta (1), Antonio Degasperis (2), Sara Lombardo (3), Matteo Sommacal (1) ((1) Northumbria University, (2) Sapienza University of Rome, (3) Loughborough University)
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Abstract:We consider the propagation of short waves which generate waves of much longer (infinite) wave-length. Model equations of such long wave-short wave 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 long wave-short wave integrable model which generalises those first proposed by Yajima-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 linearised long wave-short wave 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.
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Fluid Dynamics (physics.flu-dyn)
MSC classes: 37K40 (Primary) 37K10, 37K20, 35B35, 35Q35, 35Q55, 74J30 (Secondary)
Cite as: arXiv:2109.04296 [nlin.SI]
  (or arXiv:2109.04296v1 [nlin.SI] for this version)
  https://doi.org/10.48550/arXiv.2109.04296
Journal reference: Proc. R. Soc. A. 477, 20210408 (2021)
Related DOI: https://doi.org/10.1098/rspa.2021.0408

Submission history

From: Marcos Caso-Huerta [view email]
[v1] Thu, 9 Sep 2021 14:16:16 UTC (1,706 KB)
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