偏微分方程式セミナー: Self-similar character of the large-time asymptotics of solutions to the derivative fractional nonlinear Schrödinger equation, 林 仲夫 氏
Event Date: Nov 18, 2022
Organizer：黒田 紘敏、浜向 直
Speaker：林 仲夫 氏 (東北大学)
Title：Self-similar character of the large-time asymptotics of solutions to the derivative fractional nonlinear Schrödinger equation
Abstract：We study the large time asymptotic behavior of solutions to the Cauchy problem for the fractional derivative nonlinear Schrödinger equation in one space dimension under the non zero mass condition. Derivative nonlinear term implies the nonlinearity has the divergence form. Therefore we have mass conservation law. We define the fractional Schrödinger equation by replacing the Laplace operator by the fractional derivatives of order $\alpha$. It is known that if the order of nonlinearity is $\alpha$, then the equation has the self-similar solutions. We prove that solutions are stable in the neighborhood of the self-similar solutions.