Eduard Kirr

Eduard Kirr; P. G. Kevrekidis; Dmitry E. Pelinovsky

We consider the focusing (attractive) nonlinear Schrödinger (NLS) equation with an external, symmetric potential which vanishes at infinity and supports a linear bound state. We prove that the symmetric, nonlinear ground states must undergo a symmetry breaking bifurcation if the potential has a non-degenerate local maxima at zero. Under a generic assumption we show that the bifurcation is either a subcritical or supercritical pitchfork. In the particular case of double-well potentials with large separation, the power of nonlinearity determines the subcritical or supercritical character of the bifurcation. The results are obtained from a careful analysis of the spectral properties of the ground states at both small and large values for the corresponding eigenvalue parameter.

Eduard Kirr; Panayotis G. Kevrekidis; E. Shlizerman; Michael I. Weinstein

We consider a class of nonlinear Schrodinger/Gross–Pitaeveskii (NLS-GP) equations, i.e., NLS with a linear potential. NLS-GP plays an important role in the mathematical modeling of nonlinear optical as well as macroscopic quantum phenomena (BEC). We obtain conditions for a symmetry-breaking bifurcation in a symmetric family of states as

Eduard Kirr; Arghir Zarnescu

{\cal N}

Eduard Kirr; Michael I. Weinstein

, the squared

Eduard Kirr; Arghir Zarnescu

L^2

Smadar Karni; Eduard Kirr; Alexander Kurganov; Guergana Petrova

norm (particle number, optical power), is increased. The bifurcating asymmetric state is a “mixed mode” which, near the bifurcation point, is approximately a superposition of symmetric and antisymmetric modes. In the special case where the linear potential is a double well with well-separation L, we estimate

Scipio Cuccagna; Eduard Kirr; Dmitry E. Pelinovsky

{\cal N}_{cr}(L)

Eduard Kirr; Michael I. Weinstein

, the symmetry breaking threshold. Along the “lowest energy” symmetric branch, there is an exchange of stability from the symmetric to the asymmetric branch as

Eduard Kirr; Michael I. Weinstein

{\cal N}

Eduard Kirr; Mark Wilkinson; Arghir Zarnescu

is increased beyond