The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods

Degasperis, A.; Conforti, Matteo; Baronio, Fabio; Wabnitz, Stefan; Lombardo, Sara

doi:10.1007/s11005-010-0430-4

Cited by 18 publications

(14 citation statements)

References 34 publications

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“…Three-wave resonant interaction (TWRI) enjoys a prominent status in nonlinear science (e.g., plasma physics, optics, fluid dynamics, and acoustics) [1][2][3]. In the optical context, TWRI describes different processes such as parametric amplification, frequency conversion, transient stimulated Raman scattering (SRS) and backward or forward stimulated Brillouin scattering (SBS).…”

Section: Introductionmentioning

confidence: 99%

Optical rogue waves in parametric three-wave mixing and coherent stimulated scattering

et al. 2015

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We provide a systematic study of the rogue-wave dynamics in phase-matched weakly dispersive nonlinear media, which arise either from the parametric mixing or from the stimulated backscattering process, both of which are modeled by the three-wave resonant interaction equations. The explicit rogue-wave solutions up to the second order are presented. These solutions reveal the markedly different vector rogue-wave behaviors of the parametric and the scattering processes. In the degenerate situation where two interacting optical fields share the same group velocity, the sum of the intensities of this pair of optical wave components is spatiotemporally invariant. The close link between the existence of rogue-wave solutions and the presence of baseband modulation instability is confirmed. Finally, numerical simulations confirm that the generation of vector rogue waves is robust in the presence of spontaneous modulation instability activated by quantum noise

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Section: Introductionmentioning

confidence: 99%

Optical rogue waves in parametric three-wave mixing and coherent stimulated scattering

et al. 2015

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“…It is to be noted here that the equations used by Lavrova [4] are valid for the description of three-and four-wave interactions. Degasperis et al [17] studied the spectral theory of the resonant interaction of three waves. They presented numerical algorithm for computing the discrete eigen values as well as the scattering coefficients on the continuum spectrum.…”

Section: Derivation Of Evolution Equationsmentioning

confidence: 99%

Nonlinear Evolution Equations of Co-propagating Waves over Finite Depth Fluid

Chowdhury

Debsarma

2019

Water Waves

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Using Zakharov integral equation approach, a pair of coupled non-linear evolution equations are derived for two co-propagating weakly nonlinear gravity wave packets over finite depth fluid. Equations obtained here are not valid for resonant or quasiresonant three-wave interactions and also inapplicable for shallow water. The two evolution equations are then employed to perform modulational instability analysis of a pair of co-propagating uniform Stokes wavetrains. It is found that the relative change in phase speed of one uniform wavetrain increases with the increase in wave steepness of the other wavetrain, but it decreases with the increase in the depth of the medium. It is also observed that the growth rate of instability of one uniform wavetrain increases with the increase in wave steepness of the second wavetrain and also with the decrease in the depth of the medium.

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“…Also, the 3WRI model is well researched by lots of researchers, such as [3,4,6,13,20]. Soliton solutions of 3WRI can be classified in three main classes, depending on the boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The third class, dark-dark-dark solitons, is given in [4]. The detailed analysis of the 3WRI spectral problem presented in reference [6].…”

Section: Introductionmentioning

confidence: 99%