Sasa-Satsuma equation: Soliton on a background and its limiting cases

Bandelow, U.; Akhmediev, Nail

doi:10.1103/physreve.86.026606

Cited by 105 publications

(115 citation statements)

References 23 publications

Supporting

Mentioning

109

Contrasting

Order By: Relevance

“…The solution corresponds to a stable soliton solution although it has rational solution form. This is quite different from the rational solution presented in [12,13]. The soliton's shape is similar to the "W"-shaped soliton presented in [8].…”

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

confidence: 40%

“…Moreover, we find that the maximum value of the W-shaped soliton is nine times the background's with the condition w = 0. The corresponding solutions with frequencies in the regime 0 ≤ w ≤ c 2 are simple rational solutions, which are all different from the results presented in [12,13].…”

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

confidence: 42%

“…The Linearized Stability Analysis in [7] suggests that there are both modulational instability and stability regimes for low perturbation frequencies on the continuous wave. Based on these results, we can qualitatively know that the rational solutions reported in [12,13] are in the modulational instability regime since the solution's dynamics corresponds to rogue wave behavior. Then, the rational solution obtained here should be involved with the modulational stability regime.…”

Section: The S-s Model and Continuous Wave Backgroundmentioning

confidence: 83%

“…The rational solutions obtained in [12,13] are all in the modulational instability regime. Then, we can expect that the soliton solution could exist on the CW background in the modulational stability regime.…”

mentioning

confidence: 99%

See 3 more Smart Citations

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

Zhao

Ling

2014

Phys. Rev. E

View full text Add to dashboard Cite

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.

show abstract

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

confidence: 40%

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

confidence: 42%

Section: The S-s Model and Continuous Wave Backgroundmentioning

confidence: 83%

mentioning

confidence: 99%

See 2 more Smart Citations

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

Zhao

Ling

2014

Phys. Rev. E

View full text Add to dashboard Cite

show abstract

“…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.…”

mentioning

confidence: 99%

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

2014

View full text Add to dashboard Cite

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...

show abstract

Sasa-Satsuma equation: Soliton on a background and its limiting cases

Cited by 105 publications

References 23 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

Related Topics

Contact Info

Product

Resources

About