Research

Research Interests:

Dynamical systems
Pattern formation
Partial differential equations

Publications:

J. Daniels, "On the Existence of Periodic Traveling-Wave Solutions to Certain Systems of Nonlinear, Dispersive Wave Equations", Utah State University Graduate Theses and Dissertations, 2024.
J. Daniels, N. Nguyen, "Exact Jacobi Elliptic Solutions of the abcd-System", Water Waves. 2024.
B. Brewer, J. Daniels, N.V. Nguyen, "Exact Jacobi elliptic solutions of some models for the interaction of long and short waves", AIMS Mathematics, 2024.

Research Talks:

Introduction to Diffusive Stability, Dynamical Systems Seminar, UMN, February 2026
Graphons and their Application to Dynamical Systems, Dynamical Systems Seminar, UMN, November 2025
Topological Degree Theory for Positive Operators, Pure Math Seminar, USU, March 2024 (Slides)

Posters:

Selection of Critical Slopes in a Phase Diffusion Equation, Order and Function in Complex Systems Conference, UMN, August 2026

Awards:

2026 GAANN Fellowship from UMN
USU Math/Stat Department 2023-2024 Graduate MS Researcher of the Year Award

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