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- W3112895952 abstract "There is a lack of knowledge about the topological invariants of non-linear $d$-dimensional systems with a periodic potential. We study these systems through a classification of the linearized NLS/GP equation around their soliton solutions. Stability conditions under linearized (mode) adiabatic evolution can be interpreted topologically and we can use equivariant $mathit{K}$-theory and cohomology for their classification. On a lattice with crystallographic point group $P$, modes around stable, $P$-symmetric solitons are coarsely classified by the groups $bar{mathit{K}}_{P}^{0,tau}(mathbb{T}^d)oplus H^2(BP;mathbb{Z})$. Similarly, for $P$-symmetric gap solitons that are oscillatory stable, we have $bar{mathit{K}}_{P}^{0,tau}(mathbb{T}^d)oplus tilde{R}(P)$ instead. If we include a boundary, we can replace $bar{mathit{K}}_{P}^{0,tau}(mathbb{T}^d)$ with $mathit{K}^{-1,tau}_{P}(mathbb{T}^{d-1})$. Finally, we mention how to use these, and the spaces of soliton solutions $M_{D}(E_{gap})$ and $M_{O}(E_{gap})$ to provide global invariants for the system." @default.
- W3112895952 created "2020-12-21" @default.
- W3112895952 creator A5030119986 @default.
- W3112895952 date "2020-12-08" @default.
- W3112895952 modified "2023-09-27" @default.
- W3112895952 title "Solitons in Weakly Non-linear Topological Systems: Linearization, Equivariant Cohomology and K-theory." @default.
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- W3112895952 hasPublicationYear "2020" @default.
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