Modulation instabilities in a system of four coupled, nonlinear Schrödinger equations

Chow, K. W.; Wong, Kenneth K. Y.; Lam, Kai S

doi:10.1016/j.physleta.2008.04.057

Cited by 26 publications

(17 citation statements)

References 18 publications

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“…However, it is also known that in the case of two or more copropagating optical fields inside a nonlinear material, which is referred to as cross-phase modulation (XPM), MI can also appear both in the anomalous and normal dispersion regimes, which provides a much richer scenario of study [3]. Indeed, MI induced by XPM has been extensively studied in the literature [5,8,15,23,25,26,31,36,37,40,43,46,[48][49][50][51], including by the authors [10,11,39,41]. One of main motivations of this study is the fact that XPM is a practical mechanism of wavelength conversion and optical switching [21].…”

Section: Introductionmentioning

confidence: 99%

Modulation instability in noninstantaneous Kerr media with walk-off and cross-phase modulation for mixed group-velocity-dispersion regimes

et al. 2016

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The dynamics of the modulation instability induced by cross phase modulation is studied by considering the influence of the walk-off and noninstantaneous response effects for two copropagating optical fields travelling in the anomalous regime of dispersion. To do so, we make use of extensions of the nonlinear Schrdinger equation jointly with the Debye model for polarization, which is shown to be effective and simplified when compared to the implementation of other methods for the noninstantaneous nonlinear response. In analyzing the sideband formation, two bands are observed with different behaviors with respect to the way the maximum gain and the respective frequency vary with increasing phase mismatch. Further, we also show that the manner in which the maximum gain as well as its corresponding frequency scale with the delay parameter τ is substantially different from the cases of both fields experiencing the normal group-velocity dispersion regime and the case of mixed regimes. These facts may give rise to many new possibilities for the evolution of the modulated wave when compared to the nonanomalous cases studied in the literature.

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Section: Introductionmentioning

confidence: 99%

Modulation instability in noninstantaneous Kerr media with walk-off and cross-phase modulation for mixed group-velocity-dispersion regimes

et al. 2016

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“…For the coupled system, the usual coupled effects are cross-phase modulation terms. The linear stability analyzes indicate that the cross-phase modulation term can vary the instability regime characters [22][23][24]. Moreover, for scalar system, the velocity of the background field has no real effects on pattern structure for nonlinear localized waves, since the corresponding solutions can be correlated though trivial Galileo transformation.…”

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confidence: 99%

High-order rogue waves in vector nonlinear Schrödinger equations

Ling

Guo

Zhao³

2014

Phys. Rev. E

165

122

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We study on dynamics of high-order rogue wave in two-component coupled nonlinear Schrödinger equations. We find four fundamental rogue waves can emerge for second-order vector RW in the coupled system, in contrast to the high-order ones in single component systems. The distribution shape can be quadrilateral, triangle, and line structures through varying the proper initial excitations given by the exact analytical solutions. Moreover, six fundamental rogue wave can emerge on the distribution for second-order vector rogue wave, which is similar to the scalar third-order ones. The distribution patten for vector ones are much abundant than the ones for scalar rogue waves. The results could be of interest in such diverse fields as Bose-Einstein condensates, nonlinear fibers, and superfluids. Introduction-Rogue wave (RW) is the name given by oceanographers to isolated large amplitude wave, which occurs more frequently then expected for normal, Gaussian distributed, statistical events [1][2][3]. It depicts a unique event that seems to appear from nowhere and disappear without a trace, and can appear in a variety of different contexts [4][5][6][7]. RW has been observed experimentally in nonlinear optics by Solli group and Kibler group [8,9], water wave tank by Chabchoub group [10], and even in plasma system by Bailung group [11]. These experimental studies suggest that the rational solutions of related dynamics equations can be used to describe these RW phenomena [12,13]. Moreover, there are many different pattern structures for high-order RW [14][15][16], which can be understood as a nonlinear superposition of fundamental RW (the first order RW). Recently, many efforts are devoted to classify the hierarchy for each order RW [17,18], since these superpositions are nontrivial and admit only a fixed number of elementary RWs in each high order solution (3 or 6 fundamental ones for the second order or third order one).

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“…Assume that U, V can be expressed as a polynomial of F and basic g solitary wave function, number of respectively m, N, (3) the balance of linear and nonlinear terms of the highest order derivatives of the number, type in m=0,1,2, n=2, and so can be set: The c2=0 or d2=0, taking into account the (7) type, type the maximum number of times in G to 1 will (9) type substitution (3), by (4), (5) and 7type, can get on undetermined parameters A0, A1, A2, B1, B2, C0, C1, C2, D1, D2, K, c, C, V, nonlinear algebraic equations The elimination method for solving equations (11) in the computer algebra system was on Maple (10), to obtain the equations. By many nontrivial solutions of (9), (5) and 2type, finally got the equation 1of the seven groups of regular solitary wave solution, the obtained conclusion the following: 1) when the parameter , , meet +6 =0, equation 1has two sets of Solutions…”

Section: Solitary Wave Solutions Of the Non-linear Coupled Schrodingementioning

confidence: 99%

“…The literature [9] equation (1) discussed the integrability of the literature, using [10] elliptic function expansion method is used to solve the equation (1) some exact solutions. With the aid of symbolic computation technology, by using the F-expansion method [11,12] to solve the equation (1) exact soliton solutions.…”

Section: Introductionmentioning

confidence: 99%

Existence and Multiplicity of Solutions for a Class of Nonlinear Schrodinger- KdV Equations

Zhou¹,

Li²,

Li³

2015

TOCSJ

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In this paper, a class of coupled Riccati equations by using some special solutions of nonlinear coupled Schrodinger-KdV equations of a number of exact analytical group, obtain the precise solution and two groups of new solitary wave solutions of the equations and several general forms. With the help of computer symbolic computation technology, using F-expansion method to obtain exact solutions of the coupled Schrodinger-KdV equations, including the trigonometric function solutions, hyperbolic function solutions and Jacobian elliptic function solutions, the precise solution is widely used in plasma physics. In the past few decades, many scholars on the nonlinear Schrodinger equation and the existence of solutions of multi solution problem is studied, and the nonlinear term of the proposed restriction conditions become more and more weak. This paper firstly studies the ground state spectra with zero point solutions of Schrodinger equation. When the nonlinearity is superlinear, we give a more direct, simple and convenient method.

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Modulation instabilities in a system of four coupled, nonlinear Schrödinger equations

Cited by 26 publications

References 18 publications

Modulation instability in noninstantaneous Kerr media with walk-off and cross-phase modulation for mixed group-velocity-dispersion regimes

Modulation instability in noninstantaneous Kerr media with walk-off and cross-phase modulation for mixed group-velocity-dispersion regimes

High-order rogue waves in vector nonlinear Schrödinger equations

Existence and Multiplicity of Solutions for a Class of Nonlinear Schrodinger- KdV Equations

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