Long Wave–Short Wave Resonance in Nonlinear Negative Refractive Index Media

Chowdhury, Aref; Tataronis, J. A.

doi:10.1103/physrevlett.100.153905

Cited by 75 publications

(54 citation statements)

References 19 publications

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“…It is as well a general model that describes the interaction between a rapidly varying wave and a quasicontinuous one. In optics the LWSW resonance rules wave propagation in negative index media [31] or the optical-microwave interactions [32], whereas in hydrodynamics the LWSW resonance results from the interaction between capillary and gravity waves [33].…”

Section: Lwsw Modelmentioning

confidence: 99%

Baseband modulation instability as the origin of rogue waves

et al. 2015

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We study the existence and properties of rogue-wave solutions in different nonlinear wave evolution models that are commonly used in optics and hydrodynamics. In particular, we consider the Fokas-Lenells equation, the defocusing vector nonlinear Schrödinger equation, and the long-wave-short-wave resonance equation. We show that rogue-wave solutions in all of these models exist in the subset of parameters where modulation instability is present if and only if the unstable sideband spectrum also contains cw or zero-frequency perturbations as a limiting case (baseband instability). We numerically confirm that rogue waves may only be excited from a weakly perturbed cw whenever the baseband instability is present. Conversely, modulation instability leads to nonlinear periodic oscillations.

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Section: Lwsw Modelmentioning

confidence: 99%

Baseband modulation instability as the origin of rogue waves

et al. 2015

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“…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].…”

mentioning

confidence: 99%

“…[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].…”

mentioning

confidence: 99%

“…(1) have been arranged into a form similar to the standard NLS equation, making it clear that the nonlinearity experienced by each short wave is driven by the long-wave field, φ, rather than by |u| 2 or |v| 2 . In optical contexts, while the short-wave components u and v are called optical waves, the long-wave component φ could be thought of as the induced optical rectification [31] or the low-frequency terahertz wave [26]. As one can check, this system of equations can be readily cast into a 4 × 4 linear eigenvalue problem (one can refer to the Lax pair provided in Ref.…”

mentioning

confidence: 99%

“…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.…”

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confidence: 99%

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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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Darboux transformations for a matrix long‐wave–short‐wave equation and higher‐order rational rogue‐wave solutions

Geng

Xue

2019

Math Methods in App Sciences

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A new matrix long‐wave–short‐wave equation is proposed with the of help of the zero‐curvature equation. Based on the gauge transformation between Lax pairs, both onefold and multifold classical Darboux transformations are constructed for the matrix long‐wave–short‐wave equation. Resorting to the classical Darboux transformation, a multifold generalized Darboux transformation of the matrix long‐wave–short‐wave equation is derived by utilizing the limit technique, from which rogue wave solutions, in particular, can be obtained by employing the generalized Darboux transformation. As applications, we obtain rogue‐wave solutions of the long‐wave–short‐wave equation and some explicit solutions of the three‐component long‐wave–short‐wave model, including soliton solutions, breather solutions, the first‐order and higher‐order rogue‐wave solutions, and others by using the generalized Darboux transformation.

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Long Wave–Short Wave Resonance in Nonlinear Negative Refractive Index Media

Cited by 75 publications

References 19 publications

Baseband modulation instability as the origin of rogue waves

Baseband modulation instability as the origin of rogue waves

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

Darboux transformations for a matrix long‐wave–short‐wave equation and higher‐order rational rogue‐wave solutions

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