Localized Excitations in Nonlinear Complex Systems: Current State of the Art and Future Perspectives

Nonlinear Schrödinger Models: Continuum and Discrete Solitons and their Ghosts in PT-Symmetric Systems with Defocusing Nonlinearities.- Coding of Nonlinear States for NLS-Type Equations with Periodic Potential.- Nonreciprocal Wave Propagation Through Open, Discrete Nonlinear Schrödinger dimers.- Breather Solutions of the discrete p-Schrödinger Equation.- Bose-Einstein Condensates (BECs) and Nonlinear Optics Fragmentation of a Bose-Einstein Condensate Through Periodic Modulation of the Scattering Length.- Contact Intensity and Extended Hydrodynamics in the BCS-BEC Crossover.- N-Soliton Interactions for the Manakov System: Effects of External Potentials.- Wave Modes Trapped in Rotating Nonlinear Potentials.- Light Propagation in Two-Dimensional Plasmonic Arrays.- Nonlinear Dynamical Lattices Localized Excitations and Anisotropic Directional Ordering in a Two-Dimensional Morse Lattice Model of Cuprate Layers.- Variational Approximation to Electron Trapping by Soliton-like Localized Excitations in One-Dimensional Anharmonic Lattices.- Stability of Mode-Locked Kinks in the AC-Driven and Damped Sine-Gordon Lattice.- Spatio-Temporal Dynamics in a Ring of Coupled Pendula: Analogy with Bubbles.- Quodons and Muscovite Mica Theory of a Quodon Gas with Application to Precipitation Kinetics in Solids under Irradiation.- Energy Gain by Discrete Particle Nonlinear Lattice Excitations.- Supersonic Kinks in Coulomb Lattices.- Magnetic Metamaterials.- Stability of Discrete Breathers in Magnetic Metamaterials.- Other Nonlinear Models Checking the Validity of Truncating the Cumulant Hierarchy Description of a Small System.- Shape-Invariant Solitons in Nematic Liquid Crystals: The Influence of Noise.- Conservation Laws of a Family of Reaction-Diffusion-Convection Equations.- Effects Induced in Complex Biological Systems by High-Density Green Photons.