No stability switching at saddle-node bifurcations of solitary waves in generalized nonlinear Schrodinger equations

作者：Yang Jianke^*

来源：Physical Review E, 2012, 85(3): 037602.

DOI：10.1103/PhysRevE.85.037602

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 Schrodinger 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.

• 出版日期2012-3-30