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

Caso-Huerta, Marcos; Degasperis, A.; Lombardo, Sara; Sommacal, Matteo

doi:10.1098/rspa.2021.0408

Cited by 10 publications

(14 citation statements)

References 27 publications

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“…Models describing long wave-short wave resonant interactions arise in a variety of physical contexts, from fluid dynamics to plasma physics. In this paper, we consider the recently proposed, long wave-short wave YON (Yajima-Oikawa-Newell) model (see [11]), an integrable model featuring two arbitrary parameters, and unifying and generalizing the Yajima-Oikawa model and the Newell model.…”

Section: Discussionmentioning

confidence: 99%

“…In [11], it was shown that the YO and N Equations ( 1) and (2) need not be separately treated to investigate the short wave-long wave interaction. Indeed, these two different model equations, remarkably enough, can be combined in just one system, which we refer to as the YON model, that is itself integrable for any real value of the two arbitrary parameters α and β, namely…”

Section: Introductionmentioning

confidence: 99%

“…Despite such resonant conditions leading to small effects in capillarity-gravity wave propagation, we deem it of interest to investigate the YON model because of its potential applicability while being integrable. Indeed, it has been shown [11] that there exists a Lax pair of equations for an auxiliary function Ψ(x, t, λ) (where λ is a complex number called spectral parameter or spectral variable)…”

Section: Introductionmentioning

confidence: 99%

“…However, in the following, we will not make use of the Lax pair ( 4), and we refer the interested reader to [11], where further details on the integrable character of the system can be found.…”

Section: Introductionmentioning

confidence: 99%

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Periodic and Solitary Wave Solutions of the Long Wave–Short Wave Yajima–Oikawa–Newell Model

Caso-Huerta

Degasperis

Silva

et al. 2022

Fluids

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Models describing long wave–short wave resonant interactions have many physical applications, from fluid dynamics to plasma physics. We consider here the Yajima–Oikawa–Newell (YON) model, which was recently introduced, combining the interaction terms of two long wave–short wave, integrable models, one proposed by Yajima–Oikawa, and the other one by Newell. The new YON model contains two arbitrary coupling constants and it is still integrable—in the sense of possessing a Lax pair—for any values of these coupling constants. It reduces to the Yajima–Oikawa or the Newell systems for special choices of these two parameters. We construct families of periodic and solitary wave solutions, which display the generation of very long waves. We also compute the explicit expression of a number of conservation laws.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Periodic and Solitary Wave Solutions of the Long Wave–Short Wave Yajima–Oikawa–Newell Model

Caso-Huerta

Degasperis

Silva

et al. 2022

Fluids

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“…The system (1) has been introduced in [36], where the authors have established the integrability of the above system by providing its (3 ⇥ 3) Lax Pair.…”

Section: Introductionmentioning

confidence: 99%

Bright, dark and breather soliton solutions of the generalized long-wave short-wave resonance interaction system

Kirane

Seenimuthu

Muthusamy

2022

Preprint

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In this paper, we consider a generalized long-wave short-wave resonance interaction system, which describes the nonlinear interaction between a short-wave (SW) and a long-wave (LW). The general N -bright and N -dark soliton solutions are derived using the Hirota bilinear method and they are written in a compact way using Gram determinants. Very interestingly, the fundamental bright soliton solution of the generalized LSRI system, in general, behaves like Korteweg-deVries (KdV) soliton. However, under a special condition, it also acts like the nonlinear Schro¨dinger (NLS) soliton. The fundamental dark-soliton solution admits anti-dark, grey, and complete black soliton profiles depending on the choice of wave parameters. The results of asymptotic analysis show that both bright and dark solitons undergo elastic collision with a finite phase shift. In addition to these, we demonstrate the existence of resonance interactions among the bright solitons by tuning the phase shift regime. Furthermore, we illustrate the various types of bright and dark soliton bound states. Also, we demonstrate the different types of profiles associated with the obtained breather solution.

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The 3-wave resonant interaction model: spectra and instabilities of plane waves

Romano,

Lombardo,

Sommacal

2023

Z. Angew. Math. Phys.

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The three wave resonant interaction model (3WRI) is a non-dispersive system with quadratic coupling between the components that finds application in many areas, including nonlinear optics, fluids and plasma physics. Using its integrability, and in particular its Lax Pair representation, we carry out the linear stability analysis of the plane wave solutions interacting under resonant conditions when they are perturbed via localised perturbations. A topological classification of the so-called stability spectra is provided with respect to the physical parameters appearing both in the system itself and in its plane wave solution. Alongside the stability spectra, we compute the corresponding gain function, from which we deduce that this system is linearly unstable for any generic choice of the physical parameters. In addition to stability spectra of the same kind observed in the system of two coupled nonlinear Schrödinger equations, whose non-vanishing gain functions detect the occurrence of the modulational instability, the stability spectra of the 3WRI system possess new topological components, whose associated gain functions are different from those characterising the modulational instability. By drawing on a recent link between modulational instability and the occurrence of rogue waves, we speculate that linear instability of baseband-type can be a necessary condition for the onset of rogue wave types in the 3WRI system, thus providing a tool to predict the subsequent nonlinear evolution of the perturbation.

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

Cited by 10 publications

References 27 publications

Periodic and Solitary Wave Solutions of the Long Wave–Short Wave Yajima–Oikawa–Newell Model

Periodic and Solitary Wave Solutions of the Long Wave–Short Wave Yajima–Oikawa–Newell Model

Bright, dark and breather soliton solutions of the generalized long-wave short-wave resonance interaction system

The 3-wave resonant interaction model: spectra and instabilities of plane waves

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