Zobrazeno 1 - 10
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pro vyhledávání: '"Cole, Justin T"'
The standard understanding of topological protection from band theory is that a system's topology cannot change without first closing the bulk band gap. However, in Floquet systems, this typical definition of topological protection is one step remove
Externí odkaz:
http://arxiv.org/abs/2410.24176
Autor:
Cole, Justin T., Johnson, Troy I.
Rogue waves are fascinating large amplitude coherent structures that abruptly appear and then disappear soon after. In certain partial differential equations these waves are modeled by rational solutions. In this work we discuss approximating rogue w
Externí odkaz:
http://arxiv.org/abs/2407.04013
Autor:
Cole, Justin T., Nameika, Michael J.
A data-driven approach to calculating tight-binding models for discrete coupled-mode systems is presented. Specifically, spectral and topological data is used to build an appropriate discrete model that accurately replicates these properties. This wo
Externí odkaz:
http://arxiv.org/abs/2407.00975
The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrodinger equations. Starting from the two-dimensional extension of the well known AKNS q,r system, three diffe
Externí odkaz:
http://arxiv.org/abs/2311.04443
A honeycomb Floquet lattice with helically rotating waveguides and an interface separating two counter-propagating subdomains is analyzed. Two topologically protected localized waves propagate unidirectionally along the interface. Switching can occur
Externí odkaz:
http://arxiv.org/abs/2305.04489
Autor:
Ablowitz, Mark J., Cole, Justin T.
Publikováno v:
Physica D vol. 440 133440 (2022)
In recent years, there has been considerable interest in the study of wave propagation in nonlinear photonic lattices. The interplay between nonlinearity and periodicity has led researchers to manipulate light and discover new and interesting phenome
Externí odkaz:
http://arxiv.org/abs/2212.11993
Publikováno v:
Studies in Applied Mathematics, 2023
The propagation of localized solitons in the presence of large-scale waves is a fundamental problem, both physically and mathematically, with applications in fluid dynamics, nonlinear optics and condensed matter physics. Here, the evolution of a soli
Externí odkaz:
http://arxiv.org/abs/2211.14884
A unified method to analyze the dynamics and topological structure associated with a class of Floquet topological insulators is presented. The method is applied to a system that describes the propagation of electromagnetic waves through the bulk of a
Externí odkaz:
http://arxiv.org/abs/2206.05832
We derive the Whitham modulation equations for the nonlinear Schr\"odinger equation in the plane (2d NLS) with small dispersion. The modulation equations are derived in terms of both physical and Riemann variables; the latter yields equations of hydr
Externí odkaz:
http://arxiv.org/abs/2109.09719
Autor:
Ablowitz, Mark J., Cole, Justin T.
Publikováno v:
Physical Review Letters, vol. 127, 104101 (2021)
Rogue waves are abnormally large waves which appear unexpectedly and have attracted considerable attention, particularly in recent years. The one space, one time (1+1) nonlinear Schr\"odinger equation is often used to model rogue waves; it is an enve
Externí odkaz:
http://arxiv.org/abs/2109.05579