Analytic theory of narrow lattice solitons

Abstract

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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Cited by in corpus (7)

• Qualitative and quantitative analysis of stability and instability dynamics of positive lattice solitons
• Localized and periodic exact solutions to the nonlinear Schrodinger equation with spatially modulated parameters: Linear and nonlinear lattices
• Stability of the standing waves of the concentrated NLSE in dimension two
• Drift instability and tunneling of lattice solitons
• Band-edge solitons, Nonlinear Schrodinger / Gross-Pitaevskii Equations and Effective Media
• Bifurcation of gap solitons in periodic potentials with a sign-varying nonlinearity coefficient
• Spatial solitons rays in periodic optical lattices