Asymptotic stability of small solitary waves for the one-dimensional cubic-quintic Schrödinger equation.

Abstract: I will present two results on the asymptotic stability of small solitary waves for the one-dimensional cubic-quintic Schrödinger equation. The first result concerns the focusing-defocusing double power nonlinearity, for which the linearized operator around the small solitary waves has no internal mode. The second result concerns the more delicate case of the focusing-focusing double power nonlinearity, for which the linearized operator around the small solitary waves actually has an internal mode. The internal mode component of the solution is controlled by checking explicitly a condition related to the Fermi golden rule. We will also explain the analogies and differences with previous similar works, mainly on nonlinear wave-type models with solitons or kinks.

Posted on Jan 12, 2024 in Differential Equations, Seminars