Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2007-12-06
Nonlinear Sciences
Pattern Formation and Solitons
16 pages, 7 figures (some with multiple parts), to appear in Physical Review A
Scientific paper
10.1103/PhysRevA.78.013611
Motivated by recent proposals of ``collisionally inhomogeneous'' Bose-Einstein condensates (BECs), which have a spatially modulated scattering length, we study the existence and stability properties of bright and dark matter-wave solitons of a BEC characterized by a periodic, piecewise-constant scattering length. We use a ``stitching'' approach to analytically approximate the pertinent solutions of the underlying nonlinear Schr\"odinger equation by matching the wavefunction and its derivatives at the interfaces of the nonlinearity coefficient. To accurately quantify the stability of bright and dark solitons, we adapt general tools from the theory of perturbed Hamiltonian systems. We show that solitons can only exist at the centers of the constant regions of the piecewise-constant nonlinearity. We find both stable and unstable configurations for bright solitons and show that all dark solitons are unstable, with different instability mechanisms that depend on the soliton location. We corroborate our analytical results with numerical computations.
Bishop Alan R.
Frantzeskakis Dimitri J.
Kevrekidis Panagiotis G.
Porter Mason A.
Rodrigues A. S.
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