What I talk about when I talk about solitons

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What I talk about when I talk about solitons

김수현 0 1658
구분 수학강연회
일정 2025-05-22(목) 16:00~17:00
세미나실 129동 101호
강연자 권순식 (카이스트)
담당교수 정인지
기타
The study of solitons—localized, non-dispersive wave structures—began with a single observation by Scott Russell in 1834 and has since evolved into a rich and far-reaching mathematical theory. In this talk, I will give a brief history of soliton theory, from the discovery of solitary water waves and the integrability of the KdV equation, to the development of inverse scattering and the broader class of nonlinear dispersive equations. A central modern question in the field is the soliton resolution conjecture, which asserts that generic solutions to dispersive nonlinear equations asymptotically resolve into a finite number of solitons plus radiation. I will introduce the conjecture and discuss its current status, including rigorous results in completely integrable models and recent breakthroughs in non-integrable settings such as radial energy-critical wave equations and other models.

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