新聞標題： ( 2020-02-20 )
演講主題：Universal Wave Breaking in the Semiclassical Sine-Gordon Equation
主講人：Peter Millerr 教授 ( 密西根大學)
演講日期：2020 年2月26日(星期三) 下午14:00
摘要內容：Abstract. The sine-Gordon equation has slowly-modulated librational wave solutions that are approximated at leading-order by a Whitham averaging formalism. The Whitham modulation equations are an elliptic quasilinear system whose solutions develop singularities in finite time. We show that when the solution of the Whitham system develops a generic type of gradient catastrophe singularity, the solution of the sine-Gordon equation locally takes on a universal form, independent of initial data and described in terms of the real tritronquée solution of the Painlevé-I equation and a two-parameter family of exact solutions of sine-Gordon that represent space-time localized defects on an otherwise periodic background wave. This is joint work with Bing-Ying Lu.