Ross Parker

Ross Parker

RTG postdoctoral fellow / visiting assistant professor

Southern Methodist University

About me

I am an RTG postdoctoral fellow and visiting assistant professor in the Department of Mathematics at Southern Methodist University. I received my Ph.D. in applied mathematics from Brown University, where I worked with Björn Sandstede on the stability of nonlinear waves. In particular, I studied the existence and stability of multi-pulse solutions in continuous and discrete Hamiltonian systems.

Although I have been fascinated by mathematics as long as I can remember, it took me until my mid 30s to embrace my inner math nerd. Beforehand, I worked many different jobs, including bicycle repairperson, computer network technician, church organist, math and science tutor, and EMT.

In my spare time, I enjoy Scottish country dancing, Sacred Harp singing, playing piano and violin, and ultralight backpacking.

Interests
  • Dynamical systems
  • Nonlinear waves
  • Numerical parameter continuation
  • Network theory
Education

  • Ph.D. in applied mathematics, 2020

    Brown University

Publications

Ross Parker, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Alejandro Aceves (2023). Standing and Traveling Waves in a Model of Periodically Modulated One-dimensional Waveguide Arrays. ArXiV ePrints 2301.07631.

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Efstathios G. Charalampidis, Ross Parker, Panayotis G. Kevrekidis, Stéphane Lafortune (2023). The Stability of the b-family of Peakon Equations. Nonlinearity 36 (2023) 1192–1217.

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Ross Parker, Andrea K. Barreiro (2022). Bifurcations of a neural network model with symmetry. SIAM Journal on Applied Dynamical Systems 21 (2022) 2535-2578.

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G.A. Tsolias, Robert J. Decker, A. Demirkaya, T.J. Alexander, Ross Parker, P.G. Kevrekidis (2022). Kink-Antikink Interaction Forces and Bound States in a nonlinear Schrödinger Model with Quadratic and Quartic dispersion. ArXiV ePrints 2211.16375.

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Ross Parker, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Alejandro Aceves (2022). Revisiting Multi-breathers in the discrete Klein-Gordon equation: A Spatial Dynamics Approach. Nonlinearity 35 5714-5748.

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Ross Parker, Yannan Shen, Alejandro Aceves, John Zweck (2022). Spatiotemporal dynamics in a twisted, circular waveguide array. Studies in Applied Mathematics (2022) 1-24.

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Ross Parker, Björn Sandstede (2022). Periodic multi-pulses and spectral stability in Hamiltonian PDEs with symmetry. Journal of Differential Equations 334 (2022) 368–450.

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Ross Parker, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Alejandro Aceves (2022). Floquet solitons in square lattices: Existence, Stability and Dynamics. Physical Review E 105 (2022) 044211.

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Ross Parker, Panayotis G. Kevrekidis, Alejandro Aceves (2021). Stationary multi-kinks in the discrete sine-Gordon equation. Nonlinearity 35 (2022) 1036–1060.

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Ross Parker, Alejandro Aceves (2021). Standing wave solutions in twisted multicore fibers. Physical Review A 103 (2021) 053505.

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Ross Parker, Alejandro Aceves (2021). Multi-pulse solitary waves in a fourth-order nonlinear Schrödinger equation. Physica D: Nonlinear Phenomena 422 (2021) 132890.

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Todd Kapitula, Ross Parker, Björn Sandstede (2020). A reformulated Krein matrix for star-even polynomial operators with applications. SIAM Journal on Mathematical Analysis 52 (2020) 4705-4750.

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Ross Parker, P.G. Kevrekidis, Björn Sandstede (2020). Existence and spectral stability of multi-pulses in discrete Hamiltonian lattice systems. Physica D: Nonlinear Phenomena 408 (2020) 132414.

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Teaching

Sarah Lawrence College

  • Math 3010 : Calculus II: Further study of motion and change, Spring 2023 (syllabus)

Southern Methodist University

  • Math 3304 : Introduction to linear algebra, Fall 2022 (syllabus)
  • Math 1338 : Calculus II, Fall 2022 (syllabus)
  • Math 3302 : Calculus III: Multi–Variable and vector calculus, Spring 2022 (syllabus)
  • Math 3311 : Introduction to proof and analysis, Fall 2021 (syllabus)
  • Math 3304 : Introduction to linear algebra, Spring 2021 (syllabus)
  • Math 1337 : Calculus I, Fall 2020 (syllabus)

Brown University

Pedagogical training

Recent & Upcoming Talks

Bright and dark multi-solitons in Hamiltonian systems
Nov 11, 2022 University of Houston seminar on partial differential equations
Bright and Dark Multi-Solitons in a Fourth-Order Nonlinear Schrödinger Equation
Sep 1, 2022 SIAM Conference on Nonlinear Waves and Coherent Structures (NWCS2022)
Multi-pulse solitary waves in Hamiltonian systems: theory and numerics
Apr 8, 2022 UT Dallas computational science seminar
Standing Wave Solutions in Twisted Multicore Fibers
Nov 5, 2021 4th Annual Meeting of the SIAM Texas Louisiana Section
Periodic multi-pulses in Hamiltonian systems with symmetry
May 23, 2021 SIAM Conference on Applications of Dynamical Systems (DS21)
Instability bubbles for multi-pulse solutions to Hamiltonian systems on a periodic domain
Oct 18, 2020 3rd Annual Meeting of the SIAM Texas Louisiana Section
Multi-pulse solitary waves in Hamiltonian systems
Sep 24, 2020 SMU math colloquium
Spectral stability of periodic multi-pulses in the 5th order KdV equation
Sep 27, 2019 SIAM Conference on Applications of Dynamical Systems (DS19)
Spectral stability of multi-pulses via the Krein matrix
Apr 17, 2019 IMACS Conference on Nonlinear Evolution Equations and Wave Phenomena
Stability of double pulse solutions to the 5th order KdV equation
Feb 13, 2018 UMass Amherst applied mathematics colloquium

Code

AUTOdocker

AUTO is a publicly available software package used for continuation and bifurcation problems in ordinary differential equations and dynamical systems. It was written in 1980 and has been continually updated and maintained since then. Docker is a platform that delivers OS-level virtualization via packages called containers. Running AUTO in a Docker container allows the software to be run in a standard environment which is consistent across all platforms. You no longer have to install AUTO on your system. Interfacing with AUTO can be done using both the command line and Jupyter notebooks. This package contains Jupyter notebooks for most of the AUTO demos. These notebooks interface with AUTO to run the relevant demos, as well as plot the resulting solutions and bifurcation diagrams.