Nonlinear systems have become an area of increasing interest in the last few decades. Such nonlinear behaviour of physical systems is found nowadays in a broad range of physical systems. This includes condensed matter systems, field theoretical models, modern cosmology, and a large number of other domains of physics. One of the reasons of this increasing interest is due to the fact that many of those systems present a countable number of distinct degenerate minimal energy configurations. In many cases that degenerate structure can be described by simple models where the scalar field has a potential with two or more degenerate minima. For instance, in two or more spatial dimensions, one can describe the so-called domain walls connecting different portions of the space where the field values correspond to the different positions of the degenerate minima of the potential. In other words, the field configuration interpolates between two of those potential minima. In the context of field theory, it is quite common the appearance of solitons, which are field configurations presenting a localized and shape-invariant aspect, having a finite energy density as well as being capable of keeping their shape unaltered after a collision with another soliton. The presence of those configurations is well understood in a wide class of models, presenting or not topological nature. As examples, one can cite the monopoles, textures, strings, and kinks.

In a cosmological context, we know that nonlinear scalar field theories play a significant role in our understanding of the cosmological dynamics and structure formation. Both the inflationary epoch and the current phase of Dark Energy domination can be modelled using nonlinear scalar field models. At this point, it is important to acknowledge that the motivation in analyzing nonlinear field configurations in cosmological backgrounds has at least a threefold reason: The first comes from the fact that nonlinear configurations arise in a wide class of elementary particle models, where they are formed during phase transitions in the early Universe, and their subsequent evolution and observational signatures must therefore be understood. We know that phase transitions happened in the early universe, so the creation of topological defects is ubiquitous during this period. The second reason is related to the current observational data arising from cosmology, which has pointed out a wide number of perplexing puzzles that differ from the predictions of Λ cold dark matter (ΛCDM) model. Finally, nonlinear solutions have valuable properties giving rise to a rich variety of unusual physical phenomena, which are very different from those of more familiar systems, like the so-called solitons.

The aim of this Special Issue is to collate articles related to advances in nonlinear field theories. Original research and review articles are welcome.

Potential topics include but are not limited to the following:

• Topological defects
• Solitons
• Reheating in the early Universe
• Scalar field Dark Matter
• Bose-Einstein condensates
• Nonlinear Schrödinger equation
• Oscillons
• Vortices
• Inflationary cosmology
• Lorentz symmetry breaking
• Breathers
• Quintessence models