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A method is proposed for finding exact solutions of the nonlinear Schr~dinger equation. It uses an ansatz in which the real and imaginary parts of the unknown function are connected by a linear relation with coefficients that depend only on the time. The method consists of constructing a system of ordinary differential equations whose solutions determine(More)
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 demonstrate the generation of a supercontinuum in a 2 cm long silicon wire by pumping the wire with mid-infrared picosecond pulses in the anomalous dispersion regime. The supercontinuum extends from 1535 nm up to 2525 nm for a coupled peak power of 12.7 W. It is shown that the supercontinuum originates primarily from the amplification of background(More)
The Peregrine soliton is a localized nonlinear structure predicted to exist over 25 years ago, but not so far experimentally observed in any physical system 1. It is of fundamental significance because it is localized in both time and space, and because it defines the limit of a wide class of solutions to the non-linear Schrödinger equation (NLSE). Here, we(More)
The nonlinear Schrödinger equation (NLSE) is a central model of nonlinear science, applying to hydrodynamics, plasma physics, molecular biology and optics. The NLSE admits only few elementary analytic solutions, but one in particular describing a localized soliton on a finite background is of intense current interest in the context of understanding the(More)
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)
Stable polarization-locked temporal vector solitons are found in a saturable absorber mode-locked fiber laser with weak cavity birefringence. The system is theoretically modeled with two coupled complex Ginzburg– Landau equations that include fiber birefringence, spectral filtering, saturable gain, and slow saturable absorption. The solutions to this system(More)