Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898766 | Journal of Differential Equations | 2018 | 27 Pages |
Abstract
We consider a half-soliton stationary state of the nonlinear Schrödinger equation with the power nonlinearity on a star graph consisting of N edges and a single vertex. For the subcritical power nonlinearity, the half-soliton state is a degenerate critical point of the action functional under the mass constraint such that the second variation is nonnegative. By using normal forms, we prove that the degenerate critical point is a saddle point, for which the small perturbations to the half-soliton state grow slowly in time resulting in the nonlinear instability of the half-soliton state. The result holds for any Nâ¥3 and arbitrary subcritical power nonlinearity. It gives a precise dynamical characterization of the previous result of Adami et al. (2012) [2], where the half-soliton state was shown to be a saddle point of the action functional under the mass constraint for N=3 and for cubic nonlinearity.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Adilbek Kairzhan, Dmitry E. Pelinovsky,