Dear Colleagues,

The nonlinear Schrödinger (NLS) equation is a universal equation describing the evolution of wave envelopes in a dispersive weakly nonlinear medium. The NLS finds an important application in plasma physics, where it describes electron (Langmuir) waves, in nonlinear optics. Over the past two decades, the breadth and depth of influence of nonlinear science more generally, and of dispersive lattice systems such as the discrete nonlinear Schrödinger (DNLS) equation more specifically, have grown tremendously. Starting from the speculations on Davydov’s soliton in biophysics and nonlinear optical couplers and proposals for waveguide arrays in the 1980s, studies of the DNLS type systems passed to a different realm in the 1990s through the experimental realization of optical waveguide arrays and the observation of key theoretical predictions including discrete solitons, diffraction, Peierls barriers, multipulse features, and diffraction management. Then, they re-emerged in yet another entirely different physical incarnation in Bose–Einstein condensates (BECs) in optical lattices in the 2000s, representing one of the most exciting aspects of nonlinear phenomena in this novel state of matter. This was even more remarkable in view of the wide range of attention that BECs garnered due to their realization being awarded the Nobel prize in Physics in 2001 and their being intimately connected to superfluidity and the Nobel Prize in Physics in 2003. In the meantime, additional related aspects arose in some of the earlier settings, including but not limited to, for instance, the realization of periodic media in photorefractive crystals.

We employ methods of applied analysis, group theory and symmetry, and dynamical systems methods to analyze the existence and stability of solutions of NLS type systems.

Submit your paper and select the Journal “Symmetry” and the Special Issue “Nonlinear Schrödinger Equations and Symmetry” via: MDPI submission system. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.

Prof. Dr. Vassilis Rothos
Prof. Dr. Aydin Secer 
Guest Editors

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