Soliton-potential interactions for nonlinear Schrödinger equation in ℝ³

2017/02/14 by Deng, Qingquan, Soffer, Avy, Yao, Xiaohua
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1702.04115

Abstract

In this work we mainly consider the dynamics and scattering of a narrow soliton of NLS equation with a potential in ℝ³, where the asymptotic state of the system can be far from the initial state in parameter space. Specifically, if we let a narrow soliton state with initial velocity υ₀ to interact with an extra potential V(x), then the velocity υ₊ of outgoing solitary wave in infinite time will in general be very different from υ₀. In contrast to our present work, previous works proved that the soliton is asymptotically stable under the assumption that υ₊ stays close to υ₀ in a certain manner.

Related

• Soliton dynamics of NLS with singular potentials
• On Soliton Dynamics in Nonlinear Schrodinger Equations
• Soliton resolution for nonlinear Schrödinger type equations in the radial case
• Multi-soliton dynamics in the nonlinear Schrödinger equation
• Effective Dynamics of Solitons in the Presence of Rough Nonlinear Perturbations