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Troy I. Johnson

Publications and source records attributed to Troy I. Johnson.

2 recordsLinked to original sources
arXiv2026

Chiral solitary waves in a nonlinear topological insulator model

An outstanding challenge in the field of topological insulators is the realization of nonlinear systems that support coherent traveling waves. Highly nonlinear lattices can suffer from significant radiation losses due to Peierls-Nabarro effects. In this work a nonlinear tight-binding model that supports robust traveling edge states is proposed and examined. This system possess a nontrivial local Chern topology and soliton-like states. When a traveling solitary wave collides with a stationary mode, the two are observed to interact inelastically. These results suggest future directions for the modeling, realization, and application of nonlinear Chern insulators.

nlin.PS↗
arXiv2026

A split-step Christov method for approximating rational PDE solutions

Rational solutions of partial differential equations (PDEs) are notoriously difficult to approximate via spectral Fourier methods due to their algebraically slow decay rate. In this work we discuss approximating rational PDE solutions in a basis of orthogonal functions known as the Fourier series, allowing for the computation of its spectrum via the fast Fourier transform. Spectral differentiation matrices are derived. Several explicit fourth-order split-step integrators are derived and their performance compared. As an application, rogue wave solutions in a family of nonlinear Schrödinger equations are explored. Perturbing the constant background is found to generate rogue wave-like structures. The effects of higher-order dispersion and generalized nonlinearities are also examined.

nlin.PS↗