Analytic theory of narrow lattice solitons

Details Analytic theory of narrow lattice solitons Analytic theory of narrow lattice solitons

2007-07-11

arxiv.org/abs/0707.1589v3

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

10.1088/0951-7715/21/3/008

The profiles of narrow lattice solitons are calculated analytically using perturbation analysis. A stability analysis shows that solitons centered at a lattice (potential) maximum are unstable, as they drift toward the nearest lattice minimum. This instability can, however, be so weak that the soliton is ``mathematically unstable'' but ``physically stable''. Stability of solitons centered at a lattice minimum depends on the dimension of the problem and on the nonlinearity. In the subcritical and supercritical cases, the lattice does not affect the stability, leaving the solitons stable and unstable, respectively. In contrast, in the critical case (e.g., a cubic nonlinearity in two transverse dimensions), the lattice stabilizes the (previously unstable) solitons. The stability in this case can be so weak, however, that the soliton is ``mathematically stable'' but ``physically unstable''.

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