Search results for "soliton"

On the number of solutions of a Duffing equation

1991

The exact number of solutions of a Duffing equation with small forcing term and homogeneous Neumann boundary conditions is given. Several bifurcation diagrams are shown.

On the global dissipative and multipeakon dissipative behavior of the two-component Camassa-Holm system

2014

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/348695 Open Access The global dissipative and multipeakon dissipative behavior of the two-component Camassa-Holm shallow water system after wave breaking was studied in this paper. The underlying approach is based on a skillfully defined characteristic and a set of newly introduced variables which transform the original system into a Lagrangian semilinear system. It is the transformation, together with the associated properties, that allows for the continuity of the solution beyond collision time to be established, leading to a uniquely global d…

Trascendental Solutions of the sine-Gordon Equation

2002

Experimental and theoretical study of the nonlinear birefringence in the formation process of vector solitons in a total polarization control ring ca…

2022

Abstract In this work, we present the numerical and experimental investigation of the polarization dynamics in a free birefringence mode-locked fiber laser. The laser includes a double-pass Erbium-doped fiber amplifier and 20-m long bi-twisted fiber at a twist rate of ± 6 turns m−1 to mitigate both, linear and circular birefringence effects. We found ellipticity changes due to nonlinear birefringence in the 20-m long fiber during pulse formation and propagation. In contrast with previously reported works, the inclusion of bi-twisted fiber allows investigate the nonlinear effects independently from the linear ones. The experimental behavior was confirmed by numerical simulations based on spl…

Experimental demonstration of phase bistability in a broad-area optical oscillator with injected signal

2015

We demonstrate experimentally that a broad-area laserlike optical oscillator (a nondegenerate photorefractive oscillator) with structured injected signal displays two-phase patterns. The technique [de Valc\'arcel and Staliunas, Phys. Rev. Lett. 105, 054101 (2010)] consists in spatially modulating the injection, so that its phase alternates periodically between two opposite values, i.e., differing by $\ensuremath{\pi}$.

Hysteretic nonequilibrium Ising-Bloch transition

2005

We show that a parametrically driven cubic-quintic complex Ginzburg-Landau equation exhibits a hysteretic nonequilibrium Ising-Bloch transition for large enough quintic nonlinearity. These results help to understand the recent experimental observation of this pheomenon [A. Esteban-Martin et al., Phys. Rev. Lett. 94, 223903 (2005)].

Dissipative lattice model with exact traveling discrete kink-soliton solutions: Discrete breather generation and reaction diffusion regime

1999

International audience; We introduce a nonlinear Klein-Gordon lattice model with specific double-well on-site potential, additional constant external force and dissipation terms, which admits exact discrete kink or traveling wave fronts solutions. In the nondissipative or conservative regime, our numerical simulations show that narrow kinks can propagate freely, and reveal that static or moving discrete breathers, with a finite but long lifetime, can emerge from kink-antikink collisions. In the general dissipative regime, the lifetime of these breathers depends on the importance of the dissipative effects. In the overdamped or diffusive regime, the general equation of motion reduces to a di…

Breather Molecular Complexes in a Passively Mode‐Locked Fiber Laser

2021

International audience; Breathing solitons are nonlinear waves in which the energy concentrates in a localized and oscillatory fashion. Similarly to stationary solitons, breathers in dissipative systems can form stable bound states displaying molecule-like dynamics, which are frequently called breather molecules. So far, the experimental observation of optical breather molecules and the real-time detection of their dynamics are limited to diatomic molecules, that is, bound states of only two breathers. In this work, the observation of different types of breather complexes in a mode-locked fiber laser: multibreather molecules, and molecular complexes originating from the binding of two breat…

Subharmonic and homoclinic bifurcations in the driven and damped sine-Gordon system

1999

Abstract Chaotic responses induced by an applied biharmonic driven signal on the sine-Gordon (sG) system influenced by a constant dc-driven and the damping fields are investigated using a collective coordinate approach for the motion of the breather in the system. For this biharmonic signal, one term has a large amplitude at low frequency. Thus, the classical Melnikov method does not apply to such a system; however, we use the modified version of the Melnikov method to homoclinic bifurcations of the perturbed sG system. Additionally resonant breathers are studied using the modified subharmonic Melnikov theory. This dynamic behavior is illustrated by some numerical computations.

Instantaneous frequency measurement of dissipative soliton resonant light pulses

2016

Fil: Cuadrado-Laborde, Christian. Universidad de Valencia. Departamento de Física Aplicada y Electromagnetismo. Instituto Universitario de Ciencia de los Materiales; España Fil: Cuadrado-Laborde, Christian. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Física Rosario; Argentina Fil: Cuadrado-Laborde, Christian. Pontificia Universidad Católica Argentina. Facultad de Química e Ingeniería del Rosario; Argentina Fil: Armas Rivera, I. Benemérita Universidad Autónoma de Puebla. Facultad de Ciencias Físico Matemáticas; Mexico Fil: Carrascosa, A. Universidad de Valencia. Departamento de Física Aplicada y Electromagnetismo. Instituto Universitario de Ciencia de los Materia…