title: No stability switching at saddle-node bifurcations of solitary waves in generalized nonlinear Schrödinger equations.
abstract: Saddle-node bifurcations arise frequently in solitary waves of diverse physical systems. Previously it was believed that solitary waves always undergo stability switching at saddle-node bifurcations, just as in finite-dimensional dynamical systems. Here we show that this is not true. For a large class of generalized nonlinear Schrödinger equations with real or complex potentials, we prove that stability of solitary waves does not switch at saddle-node bifurcations. This analytical result is confirmed by numerical examples where both soliton branches are stable at saddle-node bifurcations.
authors.affiliation: Department of Mathematics and Statistics, University of Vermont, Burlington, Vermont 05401, USA.
authors.forename: Jianke
authors.initials: J
authors.lastname: Yang