arXiv subjects

Sean D. Nixon

Publications and source records attributed to Sean D. Nixon.

5 recordsLinked to original sources

arXiv2026

Topological routing in Chern insulators

Chern insulator systems are realizable in numerous physical systems and can support robust nonreciprocal transmission of energy. A routing functionality constructed from two counter-oriented Chern insulator regions, using coupled Haldane type systems is proposed. By adjusting the strength of a magnetic field and the frequency of an antenna source, it possible to steer the flow of energy: completely to the left, completely to the right, or split. Alternatively, two sources can be used to direct the flow of energy. This formulation has the potential to serve as a robust and reconfigurable component in optical transmission.

physics.optics↗

arXiv2025

Spiral Wave Solutions in Water Waves

Spiral wave solutions are found in linear and weakly nonlinear irrotational water wave equations. These unsteady spiral waves evolve from suitable initial conditions; they are not induced by external forcing. In the linear case, a long-time asymptotic result is obtained via the method of stationary phase. The asymptotic approximation is found to be in good agreement with the exact solution and reveals hyperbolic spiral structure. Numerical simulations show that these spiral waves persist in the presence of weak nonlinearity. While spiral solutions are frequently found in excitable media governed by reaction-diffusion systems, they comprise a new class of interesting two space one time dimensional solutions in fundamental linear and nonlinear dispersive wave systems.

physics.flu-dyn↗

arXiv2010

Dark solitons in mode-locked lasers

Dark soliton formation in mode-locked lasers is investigated by means of a power-energy saturation model which incorporates gain and filtering saturated with energy, and loss saturated with power. It is found that general initial conditions evolve into dark solitons under appropriate requirements also met in the experimental observations. The resulting pulses are well approximated by dark solitons of the unperturbed nonlinear Schrödinger equation. Notably, the same framework also describes bright pulses in anomalous and normally dispersive lasers.

physics.optics↗

arXiv2010

Perturbations of Dark Solitons

A method for approximating dark soliton solutions of the nonlinear Schrodinger equation under the influence of perturbations is presented. The problem is broken into an inner region, where core of the soliton resides, and an outer region, which evolves independently of the soliton. It is shown that a shelf develops around the soliton which propagates with speed determined by the background intensity. Integral relations obtained from the conservation laws of the nonlinear Schrodinger equation are used to approximate the shape of the shelf. The analysis is developed for both constant and slowly evolving backgrounds. A number of problems are investigated including linear and nonlinear damping type perturbations.

math-ph↗

arXiv2009

Soliton strings and interactions in mode-locked lasers

Soliton strings in mode-locked lasers are obtained using a variant of the nonlinear Schrodinger equation, appropriately modified to model power (intensity) and energy saturation. This equation goes beyond the well-known master equation often used to model these systems. It admits mode-locking and soliton strings in both the constant dispersion and dispersion-managed systems in the (net) anomalous and normal regimes; the master equation is contained as a limiting case. Analysis of soliton interactions show that soliton strings can form when pulses are a certain distance apart relative to their width. Anti-symmtetric bi-soltion states are also obtained. Initial states mode-lock to these states under evolution. In the anomalous regime individual soliton pulses are well approximated by the solutions of the unperturbed nonlinear Schrodinger equation, while in the normal regime the pulses are much wider and strongly chirped.

physics.optics↗