Exact stationary solutions for the translationally invariant discrete nonlinear Schrodinger equations

被引:20
|
作者
Dmitriev, S. V.
Kevrekidis, P. G.
Yoshikawa, N.
Frantzeskakis, D. J.
机构
[1] Univ Tokyo, Inst Ind Sci, Meguro Ku, Tokyo 1538505, Japan
[2] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA
[3] Univ Athens, Dept Phys, Athens 15784, Greece
关键词
D O I
10.1088/1751-8113/40/8/003
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
From a wide class of translationally invariant discrete nonlinear Schrodinger (DNLS) equations, we extract a two-parameter subclass corresponding to Kerr nonlinearity for which any stationary solution can be derived recurrently from a quadratic equation. This subclass, which incorporates the integrable (Ablowitz-Ladik) lattice as a special case, admits exact stationary solutions that are derived in terms of the Jacobi elliptic functions. Exact moving solutions for the discrete equations are also obtained. In the continuum limit, the constructed stationary solutions reduce to the exact moving solutions to the continuum NLS equation with Kerr nonlinearity. Numerical results are also presented for the special case of localized solutions, including sech (pulse, or bright soliton), tanh (kink, or dark soliton) and 1/tanh (called here inverted kink) profiles. For these solutions, we discuss their linearization spectra and their mobility. Particularly, we demonstrate that discrete dark solitons are dynamically stable for a wide range of lattice spacings, contrary to what is the case for their standard DNLS counterparts. Furthermore, the bright and dark solitons in the non-integrable, translationally invariant lattices can propagate at slow speed without any noticeable radiation.
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页码:1727 / 1746
页数:20
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