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arXiv · 1112.2583

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

Jianke Yang
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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.

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Jianke Yang. 2011-12-12. No Stability Switching at Saddle-Node Bifurcations of Solitary Waves in Generalized Nonlinear Schroedinger Equations. https://doi.org/10.1103/physreve.85.037602

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