中科院数学与系统科学研究院
数学研究所
调和分析及其应用研究中心
学术报告
调和分析和偏微分方程研讨班
报告人：刘家琪（中国科学院大学）
题 目：Long time behavior of the Sine-Gordon equation
时 间：2023.4.25（星期二）16:00-17:00
地 点：南楼 913
摘 要：We use the nonlinear steepest descent for Riemann-Hilbert problems to compute the long-time asymptotics of the solutions to the sine-Gordon equation whose initial condition belongs to some weighted Sobolev spaces. Combining the long-time asymptotics with a refined approximation argument, we analyze the asymptotic stability of multi-soliton solutions to the sine-Gordon equation in weighted energy spaces. It is known that the obstruction to the asymptotic stability of kink solutions to the sine-Gordon equation in the energy space is the existence of small breathers which is also closely related to the emergence of wobbling kinks. Our stability analysis gives a criterion for the weight which is sharp up to the endpoint so that the asymptotic stability holds.
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