Nonlinearity and Topology
arXiv:2001.10038 · doi:10.1007/978-3-030-44992-6_2
Abstract
The interplay of nonlinearity and topology results in many novel and emergent properties across a number of physical systems such as chiral magnets, nematic liquid crystals, Bose-Einstein condensates, photonics, high energy physics, etc. It also results in a wide variety of topological defects such as solitons, vortices, skyrmions, merons, hopfions, monopoles to name just a few. Interaction among and collision of these nontrivial defects itself is a topic of great interest. Curvature and underlying geometry also affect the shape, interaction and behavior of these defects. Such properties can be studied using techniques such as, e.g. the Bogomolnyi decomposition. Some applications of this interplay, e.g. in nonreciprocal photonics as well as topological materials such as Dirac and Weyl semimetals, are also elucidated.
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Cited by in corpus (5)
- Nonlinearity induced topological physics in momentum space and real space
- Probing band topology using modulational instability
- Skyrmion interactions and lattices in chiral magnets: analytical results
- Gradient catastrophe of nonlinear photonic valley-Hall edge pulses
- Bogomolny equations for the BPS Skyrme models with impurity