Recent Advances in the Theory of Nonlinear Lattices

Dear Colleagues,

The combination of nonlinearity and discreteness has long been an area of intense research, giving birth to the fundamental excitation variously called intrinsic localized modes, discrete breathers, or discrete solitons, as well as more generally providing a setting for wave instability, chaos, and pattern formation. More recently, the focus pertaining to nonlinear-lattice dynamics has broadened to encompass other fully nonlinear states, such as kinks, rogue waves, nanopterons, and pterobreathers, as well as topologically nontrivial excitations such as vortices, skyrmions, and chiral edge states that enjoy robustness due to topological protection. Similarly, lattices with carefully designed geometries can feature flat bands where compact localized states arise. In such topologically nontrivial systems, the role of nonlinearity and disorder is beginning to be explored, as is the potential utility of nonlinear and/or topological excitations to energy transport or information storage applications. Another active research arena examines parity–time symmetry (PT) and symmetry breaking in nonlinear lattices with damping and amplification featuring non-Hermitian physics.

Such recent paradigms are being investigated in a wide variety of physical systems, including (but not limited to) photonic lattices and waveguide arrays, electrical or neuronal lattices, optical lattices and matter–wave/BEC systems, MEMS structures, Josephson-junction arrays, or atomic lattices (vibrational, electronic, or spin). Review or research articles (theoretical, numerical, or experimental) exploring such nonlinear-lattice themes as outlined above in any of these systems (or beyond) would be highly welcome for this Special Issue.

Prof. Dr. Lars English
Prof. Dr. Faustino Palmero
Guest Editors

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