Ross Parker

RTG postdoctoral fellow

Southern Methodist University

Biography

I am an RTG postdoctoral fellow 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. I also collaborate with Alejandro Aceves, Todd Kapitula and Panos Kevrekidis.

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, emergency room technician, and internal medicine intern.

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

Interests

Dynamical systems
Nonlinear waves
Network theory

Education

Ph.D. in applied mathematics, 2020
Brown University

Research

Stability of solitary waves

Solitary waves are localized disturbances in a medium that maintain their shape as they propagate at a constant velocity. I study the existence and stability of multi-pulse solitary waves in Hamiltonian systems such as the fifth-order Korteweg-de Vries equation (KdV5) and the discrete nonlinear Schrodinger equation (DNLS). Multi-pulses are disturbances which resemble multiple, well separated copies of a single solitary wave.

Double pulses in KdV5 (left) and DNLS (center). Corresponding eigenvalue pattern on right.

I am interested in how the geometry of a multi-pulse solution determines its spectral stability. My research statement summarizes the work I have done on multi-pulses.