PeierlsNabarro energy surfaces and directional mobility of discrete solitons in twodimensional saturable nonlinear Schrödinger lattices
Abstract
We address the problem of directional mobility of discrete solitons in twodimensional rectangular lattices, in the framework of a discrete nonlinear Schrödinger model with saturable onsite nonlinearity. A numerical constrained NewtonRaphson method is used to calculate twodimensional PeierlsNabarro energy surfaces, which describe a pseudopotential landscape for the slow mobility of coherent localized excitations, corresponding to continuous phasespace trajectories passing close to stationary modes. Investigating the twoparameter space of the model through independent variations of the nonlinearity constant and the power, we show how parameter regimes and directions of good mobility are connected to the existence of smooth surfaces connecting the stationary states. In particular, directions where solutions can move with minimum radiation can be predicted from flatter parts of the surfaces. For such mobile solutions, slight perturbations in the transverse direction yield additional transverse oscillations with frequencies determined by the curvature of the energy surfaces, and with amplitudes that for certain velocities may grow rapidly. We also describe how the mobility properties and surface topologies are affected by inclusion of weak lattice anisotropy.
 Publication:

Physical Review E
 Pub Date:
 March 2011
 DOI:
 10.1103/PhysRevE.83.036601
 arXiv:
 arXiv:1010.1793
 Bibcode:
 2011PhRvE..83c6601N
 Keywords:

 05.45.Yv;
 42.65.Wi;
 63.20.Pw;
 63.20.Ry;
 Solitons;
 Nonlinear waveguides;
 Localized modes;
 Anharmonic lattice modes;
 Nonlinear Sciences  Pattern Formation and Solitons;
 Physics  Optics
 EPrint:
 12 pages, 8 figures, accepted in Phys. Rev. E