Self-action of light beams in nonlinear media: soliton solutions

Pushkarov, Kh. I.; Pushkarov, D. I.; Tomov, I. V.

doi:10.1007/bf00620372

Cited by 182 publications

(58 citation statements)

References 4 publications

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“…By retaining a more complete description of the linear wave operator, we have been able to apply the mathematical tools and computational techniques of Helmholtz spatial solitons to phenomena in the time domain. While the essence of this approach was suggested some three decades ago [34], it appears to have received little subsequent attention in the literature.…”

Section: Discussionmentioning

confidence: 99%

Wave envelopes with second-order spatiotemporal dispersion. II. Modulational instabilities and dark Kerr solitons

et al. 2012

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Section: Discussionmentioning

confidence: 99%

Wave envelopes with second-order spatiotemporal dispersion. II. Modulational instabilities and dark Kerr solitons

et al. 2012

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“…The VK criterion can be used to map the regions of parameter space where solution (20) can be stable (see Fig. 3).…”

Section: Stability Criterionmentioning

confidence: 99%

“…23,24,38,39 We now analyse solitons in the conditionally-stable regime (where 2 < σ < 4) in terms of the power of the input beam, denoted by P in . Typical curves in the (β, P) plane for solution (20) are shown in Fig. 3(a).…”

Section: Numerical Perturbation Analysismentioning

confidence: 99%

Helmholtz Solitons in Optical Materials With a Dual Power-Law Refractive Index

Christian

McDonald

Chamorro‐Posada³

2010

J. Nonlinear Optic. Phys. Mat.

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A nonlinear Helmholtz equation is proposed for modelling scalar optical beams in uniform planar waveguides whose nonlinear refractive index exhibits a purely-focusing dual powerlaw dependence on the electric field amplitude. Two families of exact analytical solitons, describing forward-and backward-propagating beams, are derived. These solutions are physically and mathematically distinct from those recently discovered for related nonlinearities. The geometry of the new solitons is examined, conservation laws are reported, and classic paraxial predictions are recovered in a simultaneous multiple limit. Conventional semi-analytical techniques assist in studying the stability of these nonparaxial solitons, whose propagation properties are investigated through extensive simulations.

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“…It is natural to consider models in nonlinear dynamics combining these two features, and indeed such systems likewise have physical applications [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…Then, by calculating Eq. (8) and applying in Eqs. (9) and (10), we obtain the exact solutions of Eq.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behavior and exact solution in invariant manifold for a septic derivative nonlinear Schrödinger equation

Leta

2017

Nonlinear Dyn

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In this paper, we consider a pulse dynamics in nonlinear optics (fiber-optic communications) in the presence of both self-steepening and septic nonlinear effects. Propagating profiles of the septic derivative nonlinear Schrödinger model which are isolated via coupled integrable invariants of motion, that admits exact solution, are investigated by a method of dynamical systems. By investigating the dynamical behavior and bifurcation of phase portraits of the traveling wave system, we obtain possible explicit exact parametric representations of solutions under different parameter conditions.

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Self-action of light beams in nonlinear media: soliton solutions

Cited by 182 publications

References 4 publications

Wave envelopes with second-order spatiotemporal dispersion. II. Modulational instabilities and dark Kerr solitons

Wave envelopes with second-order spatiotemporal dispersion. II. Modulational instabilities and dark Kerr solitons

Helmholtz Solitons in Optical Materials With a Dual Power-Law Refractive Index

Dynamical behavior and exact solution in invariant manifold for a septic derivative nonlinear Schrödinger equation

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