# CAREER: Long-time Behavior of Dispersive Waves

> **NSF 01003031DB NSF RESEARCH & RELATED ACTIVIT** · Georgia Tech Research Corporation (GA) · $450,000

## Abstract

Solitary waves that maintain their shape as they propagate have been observed for nearly two centuries. Today, these coherent structures are known as solitons. They arise in many nonlinear wave models in mathematics and physics, and they play an important role in understanding how complex wave patterns evolve over long times. While many of their properties are understood in special exactly solvable models, their stability, interactions, and long-time behavior remain poorly understood in many physically important settings. Basic questions remain about when such structures persist, how they interact with radiation and with one another, when collisions are elastic or inelastic, and how complicated waves simplify over time. This project studies these questions through nonlinear dispersive equations, which provide a mathematical framework for wave propagation in a wide range of systems. By advancing the mathematical understanding of solitons and related coherent structures, the project promotes progress in the mathematical sciences and strengthens foundations that are broadly relevant to wave phenomena in applied science. The project provides research training opportunities for graduate students, postdoctoral researchers, and undergraduate students through mentoring, new courses, and a summer school.

This project develops methods from partial differential equations, harmonic analysis, spectral theory, and dynamical systems to investigate the qualitative dynamics of nonlinear dispersive waves. It focuses on two closely connected directions. The first direction studies multi-soliton dynamics, including stability, global dynamics near multi-soliton configurations, and elastic and inelastic collisions. The second studies the asymptotic stability of moving kinks and related topological solitons in the presence of long-range scattering effects and internal modes. A longer-term goal is to combine these directions to analyze multi-kinks and multi-solitons under the joint infl

## Key facts

- **NSF award ID:** 2540992
- **Awardee organization:** Georgia Tech Research Corporation (GA)
- **SAM.gov UEI:** EMW9FC8J3HN4
- **PI:** Gong Chen
- **Primary program:** 01003031DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** CAREER-Faculty Erly Career Dev
- **Estimated total:** $450,000
- **Funds obligated:** $272,078
- **Transaction type:** Continuing Grant
- **Period:** 06/01/2026 → 05/31/2031

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2540992

## Citation

> US National Science Foundation, Award 2540992, CAREER: Long-time Behavior of Dispersive Waves. Retrieved via AI Analytics 2026-07-11 from https://api.ai-analytics.org/grant/nsf/2540992. Licensed CC0.

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