Gong Chen
Georgia Institute of Technology, GA·Mathematics & Statistics·Early-career
Some waves keep their shape as they travel, instead of spreading out and fading. These solitary waves, called solitons, show up in mathematical models of water waves, optics, lasers, magnetism, particle physics and Bose–Einstein condensates, an exotic state of matter predicted by quantum physics.
- Fields
Mathematics & Statistics
Physics
- Topics
solitons
solitary waves
nonlinear dispersive equations
- Grants
- 2 known grants, through May 2031
What they work on
- Determine whether multi-solitons, solutions made of several solitary waves at once, are stable and unique in nonlinear dispersive equations, using PDE, harmonic analysis and spectral theory.
- Characterize when soliton collisions are elastic (shapes preserved) or inelastic (energy lost), and describe global dynamics near multi-soliton configurations, using modulation analysis and normal form methods.
- Prove asymptotic stability of moving kinks and other topological solitons despite long-range scattering and internal vibration modes, using distorted Fourier analysis and space-time resonance methods.
- Use integrable structures, the special features of exactly solvable equations, to analyze physically important integrable systems and their perturbations, toward the soliton resolution conjecture.
- Analyze multi-kinks and multi-solitons shaped jointly by long-range interactions and internal resonances, as a step toward higher-dimensional topological solitons in mathematical physics.
More about the research
Solitons are well understood in a few special, exactly solvable equations. In many physically important settings, though, basic questions remain open. When do solitons survive over long times? How do they interact with spread-out radiation and with each other? When do they bounce off each other cleanly (elastic collisions), and when do they lose energy (inelastic collisions)? How does a complicated wave eventually simplify? The lab studies these questions through nonlinear dispersive equations, the partial differential equations (PDEs) that describe waves whose different frequencies travel at different speeds. Its two grants pursue closely connected goals.
Why it matters
This is basic mathematics. It aims to explain when coherent waves persist, how they collide, and how complicated waves simplify over time. That understanding strengthens the theoretical foundations for wave phenomena that dispersive equations describe, including water waves, optics, lasers, ferromagnetism and Bose–Einstein condensates. It could inform how scientists interpret long-time wave behavior in these physical systems.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Andrew Lawrie
University of Maryland, MD·Mathematics & Statistics
Work toward proving the soliton resolution conjecture, which predicts that generic solutions split into finitely many solitons plus radiation, without symmetry assumptions, beginning with the harmonic map heat flow in two dimensions.
Wilhelm Schlag
Yale University, CT·Mathematics & Statistics
Determine whether the kink soliton of the phi-4 model is asymptotically stable, extending a long-range scattering theory for potentials that have a threshold resonance.
Sung-Jin Oh
University of California-Berkeley, CA·Mathematics & Statistics·Early-career
Prove a forward-in-time scattering criterion for initially outgoing solutions of the energy-critical wave maps and hyperbolic Yang-Mills equations, as a step toward the soliton resolution conjecture in the one-soliton regime.
The school
Georgia Institute of Technology: 50 labs on PI Pages, $1.5B a year on research, 572 research doctorates a year.
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