On asymptotic stability of solitary waves for nonlinear Schrödinger equations
作者： Vladimir S. Buslaev , Catherine Sulem
DOI: 10.1016/S0294-1449(02)00018-5
关键词: Partial differential equation 、 Soliton 、 Eigenfunction 、 Schrödinger equation 、 Initial value problem 、 Mathematics 、 Mathematical analysis 、 Nonlinear system 、 Nonlinear Schrödinger equation 、 Riccati equation
摘要: Abstract We study the long-time behavior of solutions nonlinear Schrodinger equation in one space dimension for initial conditions a small neighborhood stable solitary wave. Under some hypothesis on structure spectrum linearized operator, we prove that, asymptotically time, solution decomposes into wave with slightly modified parameters and dispersive part described by free equation. explicitly calculate time correction.
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