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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)

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)

- 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)

- 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)

- Nail Akhmediev, Adrian Ankiewicz, J M Soto-Crespo
- Physical review. E, Statistical, nonlinear, and…
- 2009

We present a method for finding the hierarchy of rational solutions of the self-focusing nonlinear Schrödinger equation and present explicit forms for these solutions from first to fourth order. We also explain their relation to the highest amplitude part of a field that starts with a plane wave perturbed by random small amplitude radiation waves. Our work… (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.

- 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)

- A Kamagate, Ph Grelu, P Tchofo-Dinda, J M Soto-Crespo, N Akhmediev
- Physical review. E, Statistical, nonlinear, and…
- 2009

A collective variable approach is used to map domains of existence for (3+1)-dimensional spatiotemporal soliton solutions of a complex cubic-quintic Ginzburg-Landau equation. A rich variety of evolution behaviors, which include stationary and pulsating dissipative soliton dynamics, is revealed. Comparisons between the results obtained by the semianalytical… (More)