Interaction of solitons with segments with modified dispersion

Analytical solitary-wave solutions of the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with different external potentials

A large family of analytical solitary wave solutions to the generalized nonautonomous cubic-quintic nonlinear Schrödinger equation with time- and space-dependent distributed coefficients and external potentials are obtained by using a similarity transformation technique. We use the cubic nonlinearity as an independent parameter function, where a simple procedure is established to obtain different classes of potentials and solutions. The solutions exist under certain conditions and impose constraints on the coefficients depicting dispersion, cubic and quintic nonlinearities, and gain (or loss). We investigate the space-quadratic potential, optical lattice potential, flying bird potential, and potential barrier (well). Some interesting periodic solitary wave solutions corresponding to these potentials are then studied. Also, properties of a few solutions and physical applications of interest to the field are discussed. Finally, the stability of the solitary wave solutions under slight disturbance of the constraint conditions and initial perturbation of white noise is discussed numerically; the results reveal that the solitary waves can propagate in a stable way under slight disturbance of the constraint conditions and the initial perturbation of white noise.

Interaction of solitons with bond defects in discrete nonlinear Schrödinger chains

The interaction of solitons with bond defects in discrete nonlinear Schrödinger (NLS) chains is investigated. A perturbed NLS equation is derived on the basis of a microscopic model. Localized soliton-defect solutions are obtained and their stability is analyzed. Scattering of propagating solitons from bond defects is studied numerically and a variety of scattering patterns is obtained. A phase diagram is constructed showing the corresponding parametric regions.