Parametrically driven dark solitons.

We show that unlike the bright solitons, the parametrically driven kinks are immune from instabilities for all dampings and forcing amplitudes; they can also form stable bound states. In the undamped case, the two types of stable kinks and their complexes can travel with nonzero velocities.

[1]  U. Peschel,et al.  Perturbation theory for domain walls in the parametric Ginzburg-Landau equation. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  I. V. Barashenkov,et al.  Traveling solitons in the parametrically driven nonlinear Schrödinger equation. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  I. V. Barashenkov,et al.  Dynamics of the parametrically driven NLS solitons beyond the onset of the oscillatory instability , 1999 .

[4]  Xinlong Wang,et al.  OSCILLATORY PATTERNS COMPOSED OF THE PARAMETRICALLY EXCITED SURFACE-WAVE SOLITONS , 1998 .

[5]  A Sheppard,et al.  Stable topological spatial solitons in optical parametric oscillators. , 1997, Optics letters.

[6]  S. Lou,et al.  GAP SOLITONS, RESONANT KINKS, AND INTRINSIC LOCALIZED MODES IN PARAMETRICALLY EXCITED DIATOMIC LATTICES , 1996 .

[7]  Longhi.  Stable multipulse states in a nonlinear dispersive cavity with parametric gain. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[8]  S. Longhi.  Ultrashort-pulse generation in degenerate optical parametric oscillators. , 1995, Optics letters.

[9]  Zhang,et al.  Secondary Instabilities and Spatiotemporal Chaos in Parametric Surface Waves. , 1993, Physical review letters.

[10]  W. Kath,et al.  Long-term storage of a soliton bit stream by use of phase-sensitive amplification. , 1994, Optics letters.

[11]  W. Kath,et al.  Long-distance pulse propagation in nonlinear optical fibers by using periodically spaced parametric amplifiers. , 1993, Optics letters.

[12]  Kjartan Pierre Emilsson,et al.  Strong resonances of spatially distributed oscillators: a laboratory to study patterns and defects , 1992 .

[13]  Wright,et al.  Observations of localized structures in nonlinear lattices: Domain walls and kinks. , 1992, Physical review letters.

[14]  I. V. Barashenkov,et al.  Stability Diagram of the Phase-Locked Solitons in the Parametrically Driven, Damped Nonlinear Schrödinger Equation , 1991 .

[15]  Coullet,et al.  Breaking chirality in nonequilibrium systems. , 1990, Physical review letters.

[16]  Wright,et al.  Observation of a kink soliton on the surface of a liquid. , 1990, Physical review letters.

[17]  Elphick,et al.  Localized structures in surface waves. , 1989, Physical review. A, General physics.

[18]  John W. Miles,et al.  Parametrically excited solitary waves , 1984, Journal of Fluid Mechanics.

[19]  K. Subbaswamy,et al.  Numerical simulation of kink dynamics for a two-component field , 1984 .

[20]  J. Niez,et al.  Phase transition in a domain wall , 1979 .

[21]  A. Bishop,et al.  Solitary-wave solution for a complex one-dimensional field , 1976 .

[22]  A. A. Kolokolov,et al.  Stationary solutions of the wave equation in a medium with nonlinearity saturation , 1973 .