Propagation of electromagnetic soliton in antiferromagnetic medium

Daniel, M.; Veerakumar, V.

doi:10.1016/s0375-9601(02)01113-1

Cited by 49 publications

(28 citation statements)

References 27 publications

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“…The connection with long-wave models [40] has been examined too. 22 By using gauge transformations, the present system of DNLSEs can be mapped into evolution models which have direct applications to optics and plasmas. For plasma physics, the Kaup-Newell form of the coupled DNLSEs, represented by Eq.…”

Section: Discussionmentioning

confidence: 99%

“…Besides the technique of inverse scattering transform [15], the Hirota bilinear method is also applicable to these equations [17]. In addition to their great significance as examples of nonlinear dynamics in a general setting, these equations are also well known as relevant models for the properties of very narrow pulses in nonlinear optics [18,19], the propagation of Alfvén waves in magnetized plasmas [20,21], and the description of electromagnetic waves in an antiferromagnetic medium [22].…”

Section: Introductionmentioning

confidence: 99%

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Rogue waves for a system of coupled derivative nonlinear Schrödinger equations

et al. 2016

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Rogue waves (RWs) are unexpectedly strong excitations emerging from an otherwise tranquil background. The nonlinear Schrödinger equation (NLSE), a ubiquitous model with wide applications to fluid mechanics, optics and plasmas, exhibits RWs only in the regime of modulation instability (MI) of the background.For system of multiple waveguides, the governing coupled NLSEs can produce regimes of MI and RWs, even if each component has dispersion and cubic nonlinearity of opposite signs. A similar effect will be demonstrated for a system of coupled derivative NLSEs (DNLSEs), where the special feature is the nonlinear self-steepening of narrow pulses. More precisely, these additional regimes of MI and RWs for coupled DNLSEs will depend on the mismatch in group velocities between the components, as well as the parameters for cubic nonlinearity and self-steepening. RWs considered in this work differ from those of the NLSEs in terms of the amplification ratio and criteria of existence.Applications to optics and plasma physics are discussed.3

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Rogue waves for a system of coupled derivative nonlinear Schrödinger equations

et al. 2016

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“…Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characters of the participating solitons. The derivative nonlinear Schrödinger (DNLS) equation is an integrable model describing various nonlinear waves such as nonlinear Alfvén waves in space plasma(see, e.g., [1,2,3,4,5,6,7]), sub-picosecond pulses in single mode optical fibers(see, e.g., [8,9,10,11,12]), and weak nonlinear electromagnetic waves in ferromagnetic [13], antiferromagnetic [14], and dielectric[15] systems under external magnetic fields. Both of vanishing boundary conditions (VBC) and nonvanishing boundary conditions (NVBC) for the DNLS equation are physically significant.…”

Section: Introductionmentioning

confidence: 99%

N-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions

Chen¹,

Yang²,

Lam³

2006

J. Phys. A: Math. Gen.

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An explicit two-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions is derived, demonstrating details of interactions between two bright solitons, two dark solitons, as well as one bright soliton and one dark soliton. Shifts of soliton positions due to collisions are analytically obtained, which are irrespective of the bright or dark characters of the participating solitons. The derivative nonlinear Schrödinger (DNLS) equation is an integrable model describing various nonlinear waves such as nonlinear Alfvén waves in space plasma(see, e.g., [1,2,3,4,5,6,7]), sub-picosecond pulses in single mode optical fibers(see, e.g., [8,9,10,11,12]), and weak nonlinear electromagnetic waves in ferromagnetic [13], antiferromagnetic [14], and dielectric[15] systems under external magnetic fields. Both of vanishing boundary conditions (VBC) and nonvanishing boundary conditions (NVBC) for the DNLS equation are physically significant. For problems of nonlinear Alfvén waves, weak nonlinear electromagnetic waves in magnetic and dielectric media, waves propagating strictly parallel to the ambient magnetic fields are modelled by VBC while those oblique waves are modelled by NVBC. In optical fibers, pulses under bright background waves are modelled by NVBC.

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“…One of them, the derivative nonlinear Schrödinger equation, can be used to describe such physical phenomena as the Alfvén waves in space plasma [18][19][20][21][22][23], femtosecond pulses in the single-mode optical fibers [24][25][26][27], weak nonlinear electromagnetic waves in (anti-)ferromagnetic or dielectric systems under the external magnetic fields [28][29][30]. With the inhomogeneity of the real plasma environment (i.e., the fluctuations of the density, temperature and magnetic fields) considered [31][32][33], attention has been paid to the variable-coefficient derivative nonlinear Schrödinger (vc-DNLS) equations [34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Solitonic interactions, Darboux transformation and double Wronskian solutions for a variable-coefficient derivative nonlinear Schrödinger equation in the inhomogeneous plasmas

et al. 2011

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By symbolic computation we study a variable-coefficient derivative nonlinear Schrödinger (vc-DNLS) equation describing nonlinear Alfvén waves in inhomogeneous plasmas. Based on the Lax pair of the vc-DNLS equation, the N-fold Darboux transformation is constructed via a gauge transformation and the reduction technique. Multi-solitonic solutions in terms of the double Wronskian for the vc-DNLS equation are obtained. Two-and three-solitonic interactions are analyzed graphically, i.e., overtaking, head-on and parallel interactions. Plasma streaming and inhomogeneous magnetic field control the amplitudes and velocities of the solitonic waves, respectively. The nonuniform density affects the amplitudes of the solitonic waves. The effects of the spectral parameters on the dynamics of the two-solitonic waves are discussed.Our results might facilitate the analytic investigation on certain inhomogeneous systems in the Earth's magnetosphere, solar winds, planetary bow shocks, dusty cometary tails and interplanetary shocks.

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Propagation of electromagnetic soliton in antiferromagnetic medium

Cited by 49 publications

References 27 publications

Rogue waves for a system of coupled derivative nonlinear Schrödinger equations

Rogue waves for a system of coupled derivative nonlinear Schrödinger equations

N-soliton solution for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions

Solitonic interactions, Darboux transformation and double Wronskian solutions for a variable-coefficient derivative nonlinear Schrödinger equation in the inhomogeneous plasmas

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