Optical Solitons

Abdullaev, F. Kh.; Darmanyan, S.; Khabibullaev, P. K.

doi:10.1007/978-3-642-87716-2

Cited by 121 publications

(134 citation statements)

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“…Let us set α 1 = θ(y m , z) as the amplitude of the director solution (5) at z, which occurs at (6). When the nematicon is at the centre of the cell ξ = 0, then the director beam has a symmetric form too with y m = 0.…”

Section: One Space Dimensionmentioning

confidence: 99%

“…The electric field amplitude is a = 0.219 and the director amplitude is α 1 = 0.188. Using the initial values for the parameters and ξ = 3.55 in (6) gives y m = 3.24. Hence the analytical expression for the location of the director beam gives an excellent prediction which closely matches the numerically obtained location.…”

Section: A 1d Nematicon Bouncing In a Cellmentioning

confidence: 99%

“…In optics, in particular, they have received much attention due to the versatile nature of self-induced waveguides, a concept amenable to applications in applied nonlinear optics and communications, for which all-optical switching and routing could play an important role in future generations of signal processors [6][7][8][9]. In this scenario, nematicons -i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Spatial solitons are ubiquitous as they are found and studied in fluids, plasmas, Bose-Einstein condensates, electronics and optics [1][2][3][4][5][6][7]. In optics, in particular, they have received much attention due to the versatile nature of self-induced waveguides, a concept amenable to applications in applied nonlinear optics and communications, for which all-optical switching and routing could play an important role in future generations of signal processors [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

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Modulation analysis of boundary-induced motion of optical solitary waves in a nematic liquid crystal

et al. 2009

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Section: One Space Dimensionmentioning

confidence: 99%

Section: A 1d Nematicon Bouncing In a Cellmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modulation analysis of boundary-induced motion of optical solitary waves in a nematic liquid crystal

et al. 2009

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“…In fact, Ref. [23] applied this procedure to obtain a solution of the single-component nonlinear Schrödinger equation (NLSE). But solutions from the N-phase theta functions have the so-called "effectivization" problem, which is related to extracting the physical solutions by taking proper initial conditions [24,10].…”

Section: Introductionmentioning

confidence: 99%

Soliton on a cnoidal wave background in the coupled nonlinear Schrödinger equation

Shin¹

2004

J. Phys. A: Math. Gen.

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An application of the Darboux transformation on a cnoidal wave background in the coupled nonlinear Schrödinger equation gives a new solution which describes a soliton moving on a cnoidal wave. This is a generalized version of the previously known soliton solutions of dark-bright pair. Here a dark soliton resides on a cnoidal wave instead of on a constant background. It also exhibits a new types of soliton solution in a self-focusing medium, which describes a breakup of a generalized darkbright pair into another generalized dark-bright pair and an "oscillating" soliton. We calculate the shift of the crest of the cnoidal wave along a soliton and the moving direction of the soliton on a cnoidal wave.

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Numerical study of two‐dimensional stochastic NLS equations

Barton-Smith¹,

Debussche²,

Menza³

2005

Numerical Methods Partial

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In this article, we numerically solve the two‐dimensional stochastic nonlinear Schrödinger equation in the case of multiplicative and additive white noises. The aim is to investigate their influence on well‐known deterministic solutions: stationary states and blowing‐up solutions. In the first case, we find that a multiplicative noise has a damping effect very similar to diffusion. However, for small amplitudes of the noise, the structure of solitary state is still localized. In the second case, a local refinement algorithm is used to overcome the difficulty arising for the computation of singular solutions. Our experiments show that multiplicative white noise stops the deterministic blow‐up that occurs in the critical case. This extends the results of Debussche and Di Menza (Physica D, 162(3–4) 2002, 131–154) in the one‐dimensional case. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential, 2005.

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Optical Solitons

Cited by 121 publications

References 0 publications

Modulation analysis of boundary-induced motion of optical solitary waves in a nematic liquid crystal

Modulation analysis of boundary-induced motion of optical solitary waves in a nematic liquid crystal

Soliton on a cnoidal wave background in the coupled nonlinear Schrödinger equation

Numerical study of two‐dimensional stochastic NLS equations

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