No Stability Switching at Saddle-Node Bifurcations of Solitary Waves in Generalized Nonlinear Schroedinger Equations

摘要

Saddle-node bifurcations arise frequently in solitary waves of diversephysical systems. Previously it was believed that solitary waves always undergostability switching at saddle-node bifurcations, just as in finite-dimensionaldynamical systems. Here we show that this is not true. For a large class ofgeneralized nonlinear Schr\"odinger equations with real or complex potentials,we prove that stability of solitary waves does not switch at saddle-nodebifurcations. This analytical result is confirmed by numerical examples whereboth soliton branches are stable at saddle-node bifurcations.