Standing waves for nonlinear Schrödinger equations with singular potentials

Stability and instability of standing waves for nonlinear Schrödinger equations

Higher Dimensional Vortex Standing Waves for Nonlinear Schrödinger Equations

We study standing wave solutions to nonlinear Schrödinger equations, on a manifold with a rotational symmetry, which transform in a natural fashion under the group of rotations. We call these vortex solutions. They are higher dimensional versions of vortex standing waves that have been studied on the Euclidean plane. We focus on two types of vortex solutions, which we call spherical vortices an...

Stability switching at transcritical bifurcations of solitary waves in generalized nonlinear Schrödinger equations

a r t i c l e i n f o a b s t r a c t Linear stability of solitary waves near transcritical bifurcations is analyzed for the generalized nonlinear Schrödinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions. Bifurcation of linear-stability eigenvalues associated with this transcritical bifurcation is analytically calculated. Based on this e...

Multiple Semiclassical Standing Waves for a Class of Nonlinear Schrödinger Equations

Conditions and Stability Analysis for Saddle-Node Bifurcations of Solitary Waves in Generalized Nonlinear Schrödinger Equations

Saddle-node bifurcations of solitary waves in generalized nonlinear Schrödinger equations with arbitrary forms of nonlinearity and external potentials in arbitrary spatial dimensions are analyzed. First, general conditions for these bifurcations are derived. Second, it is shown analytically that the linear stability of these solitary waves does not switch at saddle-node bifurcations, which is i...