Generating mechanism for higher-order rogue waves

He, Jingsong; Zhang, H. R.; Wang, L. H.; Porsezian, K.; Fokas, A. S.

doi:10.1103/physreve.87.052914

Cited by 343 publications

(264 citation statements)

References 50 publications

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“…3. The distribution shape is identical with the well-known fundamental RW solution with highest peak value of the simplified NLS [1,[22][23][24]. These characters are different from the fundamental W-shaped soliton in Case 1.…”

Section: Two Explicit Cases For the Rational W-shaped Soliton Somentioning

confidence: 56%

“…Notably, we find a new type rational solution on continuous background with some certain conditions on the background's amplitude and frequency c ≥ 2w. We find that the rational solution does not correspond to rogue wave, in contrast to the ones of the simplified NLS [1,[22][23][24]. Its dynamics corresponds to soliton's which has a stable distribution shape with evolution, and the distribution shape like a "W" which has one hump and two valleys on the hump's two sides.…”

Section: The S-s Model and Continuous Wave Backgroundmentioning

confidence: 93%

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Rational W-shaped solitons on a continuous-wave background in the Sasa-Satsuma equation

Zhao

Ling

2014

Phys. Rev. E

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We study localized wave on continuous wave background analytically in a nonlinear fiber with higher order effects such as higher order dispersion, Kerr dispersion, and stimulated inelastic scattering. We present an exact rational W-shaped soliton solutions, whose structural properties depend on the frequency of the background field. The hump value increase with the decrease of the background frequency in the certain regime. The highest value of the W-shaped soliton can be nine times the background's, and the distribution shape is identical with the one of well-known eyes-shaped rogue wave with its maximum peak. The numerical stimulations indicate that the W-shaped soliton is stable with small perturbations.

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Section: Two Explicit Cases For the Rational W-shaped Soliton Somentioning

confidence: 56%

Section: The S-s Model and Continuous Wave Backgroundmentioning

confidence: 93%

Rational W-shaped solitons on a continuous-wave background in the Sasa-Satsuma equation

Zhao

Ling

2014

Phys. Rev. E

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“…The latter behavior could be linked to the existence of high-order multiple rogue wave solutions of Eq. (1), in analogy to the multiple rogue wave solutions found within the scalar NLS equation [46][47][48]. These subsequent multiple rogue waves could also be triggered by the onset of MI, which promotes quasiperiodic structures by patterning the continuous-wave background.…”

Section: Fig 2 (Color Online)mentioning

confidence: 99%

Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance

2014

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The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics. [4,5], these extreme wave events were also observed in a wide class of physical systems, including capillary waves and surface ripples [6,7], plasmas [8], optical fibers [9,10], mode-locked lasers [11], and filaments [12]. These studies have uncovered general features of nonlinearity and complexity shared by rogue waves, e.g., they are extremely large and steep compared with typical events, occur in a nonlinear medium, and follow an unusual L-shaped statistics [9,[11][12][13]. Despite these diverse features, mathematical solutions of rogue waves can be expressed as rational functions localized in both space and time. One typical example is the Peregrine soliton [14], a well-known rogue wave prototype in various experimental fields [4,8,10], which is the lowest-order rational solution to the nonlinear Schrödinger (NLS) equation.Following the need to model complex physical systems more precisely, it has become important to study rogue wave phenomena beyond the framework of the NLS equation. Recent developments have taken into account dissipative effects [11,15,16], included higher-order nonlinear terms [17][18][19], or considered the coupling between several fields [20][21][22][23][24][25]. The latter investigations have led to the discovery of intricate rogue wave structures that are generally unattainable in the scalar models. In particular, we showed in Ref.[25] that the long-wave-short-wave (LWSW) resonance interaction can result in stable dark and bright rogue waves in spite of the onset of modulational instability (MI). This finding brings about the possibility to observe dark rogue waves in LWSW resonance systems such as negative index media [26] and capillary-gravity waves [6,27].Basically, the LWSW resonance is a general parametric process that manifests when the group velocity of the short wave matches the phase velocity of the long wave [28]. It has been predicted in different disciplines such as fluid dynamics [27], plasma physics [29], oceanography [30], and nonlinear optics [26,31]. Early works showed that both the LWSW and the NLS equations could be obtained from the same Davey-Stewartson system under the appropriate parameter conditions [27,32,33], although the former is currently less popular in use than the latter.In fact, it is possible to co...

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“…The RWs have also been observed experimentally in physical systems such as water wave tank [22], capillary waves [23] and nonlinear optics [5,24]. Several theoretical studies on the dynamics of RWs in nonlinear fiber optics [25,26], plasma physics [27], laser-plasma interactions [28], and even econophysics [29], described by scalar NLS equation, have been made in recent times. Now, as mentioned in the beginning, the dynamics of a cigar shaped BEC at absolute zero temperature is usually described by the mean-field GP equation (1), which is a generalized form of the ubiquitous constant coefficient NLS equation (2), for the wave function of the condensate.…”

Section: Introductionmentioning

confidence: 99%

Manipulating matter rogue waves and breathers in Bose-Einstein condensates

et al. 2014

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We construct higher order rogue wave solutions and breather profiles for the quasi-one-dimensional Gross-Pitaevskii equation with a time-dependent interatomic interaction and external trap through the similarity transformation technique. We consider three different forms of traps, namely (i) timeindependent expulsive trap, (ii) time-dependent monotonous trap and (iii) time-dependent periodic trap. Our results show that when we change a parameter appearing in the time-independent or time-dependent trap the second and third-order rogue waves transform into the first-order like rogue waves. We also analyze the density profiles of breather solutions. Here also we show that the shapes of the breathers change when we tune the strength of trap parameter. Our results may help to manage rogue waves experimentally in a BEC system.

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Generating mechanism for higher-order rogue waves

Cited by 343 publications

References 50 publications

Rational W-shaped solitons on a continuous-wave background in the Sasa-Satsuma equation

Rational W-shaped solitons on a continuous-wave background in the Sasa-Satsuma equation

Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance

Manipulating matter rogue waves and breathers in Bose-Einstein condensates

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