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This paper reviews the latest advances in the area of multi-soliton complexes (MSCs). We present exact analytical solutions of coupled nonlinear Schrr odinger equations, which describe multi-soliton complexes and their interactions on top of a background in media with self-focusing or self-defocusing Kerr-like nonlinearities. We p r e s e n t n umerical… (More)

- N Akhmediev, J M Soto-Crespo, G Town
- Physical review. E, Statistical, nonlinear, and…
- 2001

The complex Ginzburg-Landau equation (CGLE) is a standard model for pulse generation in mode-locked lasers with fast saturable absorbers. We have found complicated pulsating behavior of solitons of the CGLE and regions of their existence in the five-dimensional parameter space. We have found zero-velocity, moving and exploding pulsating localized… (More)

- J M Soto-Crespo, N Akhmediev, A Ankiewicz
- Physical review letters
- 2000

We present three novel pulsating solutions of the cubic-quintic complex Ginzburg-Landau equation. They describe some complicated pulsating behavior of solitons in dissipative systems. We study their main features and the regions of parameter space where they exist.

We observe polarization-locked vector solitons in a mode-locked fiber laser. Temporal vector solitons have components along both birefringent axes. Despite different phase velocities due to linear birefringence, the relative phase of the components is locked at 6p͞2. The value of 6p͞2 and component magnitudes agree with a simple analysis of the Kerr… (More)

- J M Soto-Crespo, Ph Grelu, N Akhmediev, N Devine
- Physical review. E, Statistical, nonlinear, and…
- 2007

We show, numerically, that coupled soliton pairs in nonlinear dissipative systems modeled by the cubic-quintic complex Ginzburg-Landau equation can exist in various forms. They can be stationary, or they can pulsate periodically, quasiperiodically, or chaotically, as is the case for single solitons. In particular, we have found various types of vibrating… (More)

Using the method of moments for dissipative optical solitons, we show that there are two disjoint sets of fixed points. These correspond to stationary solitons of the complex cubic–quintic Ginzburg–Landau equation with concave and convex phase profiles respectively. Numerical simulations confirm the predictions of the method of moments for the existence of… (More)

- A Chabchoub, N Hoffmann, M Onorato, G Genty, J M Dudley, N Akhmediev
- Physical review letters
- 2013

We report the experimental observation of multi-bound-soliton solutions of the nonlinear Schrödinger equation (NLS) in the context of hydrodynamic surface gravity waves. Higher-order N-soliton solutions with N=2, 3 are studied in detail and shown to be associated with self-focusing in the wave group dynamics and the generation of a steep localized carrier… (More)

- Nail Akhmediev, J M Soto-Crespo, Philippe Grelu
- Chaos
- 2007

Nonlinear dissipative systems display the full (3+1)D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic Ginzburg-Landau equation model. Numerical simulations reveal the existence of stationary bell-shaped (3+1)D solitons for both anomalous and normal chromatic dispersion regimes,… (More)

- J M Dudley, G Genty, F Dias, B Kibler, N Akhmediev
- Optics express
- 2009

Numerical simulations of the onset phase of continuous wave supercontinuum generation from modulation instability show that the structure of the field as it develops can be interpreted in terms of the properties of Akhmediev Breathers. Numerical and analytical results are compared with experimental measurements of spectral broadening in photonic crystal… (More)

- A Chabchoub, N P Hoffmann, N Akhmediev
- Physical review letters
- 2011

The conventional definition of rogue waves in the ocean is that their heights, from crest to trough, are more than about twice the significant wave height, which is the average wave height of the largest one-third of nearby waves. When modeling deep water waves using the nonlinear Schrödinger equation, the most likely candidate satisfying this criterion is… (More)