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

4 pages, 2 figures

References in corpus (1)

• From nonlocal gap solitary waves to bound states in periodic media

Cited by in corpus (6)

• Spontaneous symmetry breaking and ghost states supported by the fractional nonlinear Schrödinger equation with focusing saturable nonlinearity and PT-symmetric potential
• Stability analysis for pitchfork bifurcations of solitary waves in generalized nonlinear Schroedinger equations
• Quasi-one-dimensional harmonically trapped quantum droplets
• Stability switching at transcritical bifurcations of solitary waves in generalized nonlinear Schroedinger equations
• A normal form for Hamiltonian-Hopf bifurcations in generalized nonlinear Schrodinger equations
• Numerical Computations for Bifurcations and Spectral Stability of Solitary Waves in Coupled Nonlinear Schrödinger Equations