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Time-localized solitary wave solutions of the one-dimensional complex Ginzburg-Landau equation ͑CGLE͒ are analyzed for the case of normal group-velocity dispersion. Exact soliton solutions are found for both the cubic and the quintic CGLE. The stability of these solutions is investigated numerically. The regions in the parameter space in which stable… (More)

We extend the concept of internal mode to envelope solitons and show that this mode is responsible for long-lived, weakly damped periodic oscillations of the soliton amplitude observed in numerical simulations. We present analytical and numerical results for solitons of the generalized nonlinear S chr6dinger equation and analyze the example of the… (More)

Nonlinear theory describing the instability-induced dynamics of dark solitons in the generalized nonlinear Schrödinger equation is presented. Equations for the evolution of an unstable dark soliton, including its transformation into a stable soliton, are derived using a multiscale asymptotic technique valid near the soliton instability threshold. Results of… (More)

- Robert W. Micallef, Vsevolod V. Afanasjev, Yuri S. Kivshar, John D. Love
- 1996

It is shown that self-guided optical beams with power-law asymptotics, i.e., algebraic optical solitons, can be regarded as a special case of sech-type solitons ͑i.e. solitons with exponentially decaying asymptotics͒ in the limit where the beam propagation constant coincides with the threshold for linear wave propagation. This leads to the conjecture that… (More)

- Z Chen, M Segev, T H Coskun, D N Christodoulides, Y S Kivshar, V V Afanasjev
- Optics letters
- 1996

We report the observation of incoherently coupled dark-bright spatial soliton pairs in a biased bulk photorefractive crystal. When such a pair is decoupled, the dark component evolves into a triplet structure, whereas the bright one decays into a self-defocusing beam.

- V V Afanasjev, Y S Kivshar, C R Menyuk
- Optics letters
- 1996

Third-order dispersion has a detrimental effect on dark solitons, leading to resonant generation of growing soliton tails and soliton decay. This effect is shown to be much stronger than that for bright solitons.

- V V Afanasjev, P L Chu, Y S Kivshar
- Optics letters
- 1997

The concept of soliton internal mode is introduced to explain quantitatively the long-lived oscillations of self-guided beams, or breathing spatial solitons. Cubic-quintic nonlinearity is considered in detail, and it is shown that the existence of the internal mode affects strongly the beam propagation in non-Kerr media, leading to oscillatory dependence of… (More)

- Y S Kivshar, V V Afanasjev
- Optics letters
- 1996

It is shown that dark solitons display an inherent instability for a strong saturation of the nonlinear refractive index provided that the background intensity exceeds a certain critical value. Such an instability manifests itself as a drift of a black soliton that transform into a gray soliton and radiation.

- Y S Kivshar, V V Afanasjev
- Optics letters
- 1991

It is demonstrated analytically and numerically that dark solitons always disappear owing to the stimulated Raman effect. Instead of dark solitons, the stable propagation of optical kinks on the cw background in the region of the normal group-velocity dispersion is possible.

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