Ebb and Flow: USU Inaugural Professor Applies Steadfast Tenacity to Nonlinear Wave Challenges

In 1834, while contemplating the most efficient design for a canal boat, Scottish engineer John Scott Russell watched as a horse-drawn barge hit an underwater obstruction in an Edinburgh canal and suddenly stopped. While the vessel halted, the mass of water surrounding it quickly rose around the boat’s prow and rapidly surged forward into what Russell described as “a rounded, smooth and well-defined heap of water.”

Russell, on horseback, followed that heap of water at a nine-mile-per-hour clip for nearly two miles, until it gradually disappeared.

Fascinated by what he described as the “Wave of Translation,” Russell wrote extensively of his observation, now known in fluid dynamics as “Russell’s solitary wave.” The phenomenon of wave behavior has spawned much-debated theories, which have sparked animated discussion and controversy among scientists, mathematicians and engineers for decades.

Utah State University mathematician Nghiem Nguyen shares Russell’s fascination with wave theory and, like Russell, has also fostered provocative inquiry — particularly with his breakthrough research challenging the validity of the Nonlinear Schrödinger-Korteweg-de Vries (NLS-KdV) system, a collection of partial differential equations modeling interactions between short and long dispersive waves. Nguyen shared his professional journey, along with Russell’s canal wave story, during his Oct. 15 presentation, “A Little Taste of Nonlinear Waves and All That,” during the university’s 2024 Inaugural Professor Lecture Series.

Hosted at USU’s Nora Eccles Harrison Museum of Art, Nguyen’s lecture is among a succession of fall gatherings coordinated by the Provost’s Office to highlight the accomplishments and academic journeys of faculty who have been promoted to full professor during the past year.

“With his research, Dr. Nguyen has introduced a paradigm shift in his field,” said John Stevens, head of USU’s Department of Mathematics and Statistics, who introduced Nguyen at the gathering. “This bold, new direction has garnered praise from leading scholars, who describe Dr. Nguyen’s work as brave and exciting.”

Nguyen said pursuing research on the NLS-KdV System, about which he challenged long-held and controversial assertions, wasn’t easy.

“Though widely studied, the nonlinear version of the NLS-KdV system has never been derived, even though many scholars assume it has,” Nguyen said. “It’s been somewhat awkward to point this out at professional conferences, since many in the mathematics community have written papers based on this false assumption.”

Nguyen noted his predecessor Russell also endured skepticism from colleagues, but stood by his wave observations and experiments, proclaiming, “I know what I saw.”

“For the last several years, I have proposed some other systems, where every step is rigorously justified, to study the nonlinear interaction of short and long waves, in place of the NLS-KdV system,” he said.

Nguyen’s tenacity has paid off and his research has garnered international acclaim.

“I try to instill this same determination, confidence and resiliency in my students,” he said. “I urge them to pay attention to details, write papers in a concise and coherent way, and to rigorously justify all the steps as they make assertions.”

Nguyen reinforces these ideas as the mentor to USU teams competing in the annual William Lowell Putnam Mathematical Competition, a premier mathematics competition for undergraduate scholars in the United States and Canada. For the past several years, he’s coached student teams that have placed in the top quartile.

“In 2023, our team scored in the top 17 percent of competitors and we advanced in the rankings from previous years,” Nguyen said. “That’s an impressive improvement, which shows we’re learning from experience.”

A recipient of multiple awards, Nguyen has been recognized as a College of Science Undergraduate Research Mentor of the Year and as Faculty Mentor of the Year. He also serves on the committee for the college’s Science Unwrapped public outreach program.

Born in Vietnam, Nguyen immigrated to the United States as a teenager.

“I took the SAT college entrance exam as I was just beginning to learn English,” he said. “I managed to get a passing score on the verbal portion of the test, but thankfully, I excelled in the mathematics portion,” he said.

Nguyen began his college journey at New York University, from which he earned bachelor’s and master’s degrees in mathematics. He completed a doctoral degree from the University of Illinois at Chicago, and joined USU’s faculty in 2008.

“Utah State has been a wonderful and encouraging academic home,” he said.