Two-dimensional solitons in media with stripe-shaped nonlinearity modulation

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print)

DOI:https://doi.org/10.1103/PHYSREVE.82.046602· OSTI ID:21464554

Hung, Nguyen Viet; Zin, Pawel ^[1]; Trippenbach, Marek ^[2]; Malomed, Boris A ^[3]

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1. Soltan Institute for Nuclear Studies, Hoza 69, PL-00-681 Warsaw (Poland)
2. Institute of Theoretical Physics, Physics Department, Warsaw University, Hoza 69, PL-00-681 Warsaw (Poland)
3. Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

We introduce a model of media with the cubic attractive nonlinearity concentrated along a single or double stripe in the two-dimensional (2D) plane. The model can be realized in terms of nonlinear optics (in the spatial and temporal domains alike) and BEC. It is known from recent works that search for stable 2D solitons in models with a spatially localized self-attractive nonlinearity is a challenging problem. We make use of the variational approximation (VA) and numerical methods to investigate conditions for the existence and stability of solitons in the present setting. The result crucially depends on the transverse shape of the stripe: while the rectangular profile supports stable 2D solitons, its smooth Gaussian-shaped counterpart makes all the solitons unstable. This difference is explained, in particular, by the VA. The double stripe with the rectangular profile admits stable solitons of three distinct types: symmetric and asymmetric ones with a single-peak, and double-peak symmetric solitons. The shape and stability of the single-peak solitons of either type are accurately predicted by the VA. Collisions between identical stable solitons are briefly considered too, by means of direct simulations. Depending on the collision velocity, we observe excitation of intrinsic oscillations of the solitons, or their decay, or the collapse (catastrophic self-focusing).

• OSTI ID: 21464554
• Journal Information: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics (Print), Vol. 82, Issue 4; Other Information: DOI: 10.1103/PhysRevE.82.046602; (c) 2010 The American Physical Society; ISSN 1539-3755
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
APPROXIMATIONS
ASYMMETRY
COMPUTERIZED SIMULATION
DECAY
EXCITATION
MODULATION
NONLINEAR OPTICS
NONLINEAR PROBLEMS
OSCILLATIONS
SOLITONS
STABILITY
SYMMETRY
TWO-DIMENSIONAL CALCULATIONS
VARIATIONAL METHODS
CALCULATION METHODS
ENERGY-LEVEL TRANSITIONS
OPTICS
QUASI PARTICLES
SIMULATION