D.E. Pelinovsky and M. Plum
Stability of black solitons in optical systems with intensity-dependent dispersion
SIAM Journal of Mathematical Analysis 56 (2024) 2521-2568
Abstract:
Black solitons are identical in the nonlinear Schrodinger (NLS) equation with intensity-dependent dispersion
and the cubic defocusing NLS equation. We prove that the intensity-dependent dispersion introduces new properties
in the stability analysis of the black soliton. First, the spectral stability problem possesses only isolated
eigenvalues on the imaginary axis. Second, the energetic stability argument holds in Sobolev spaces with exponential weights.
Third, the black soliton persists with respect to addition of a small decaying potential and remains spectrally stable
when it is pinned to the minimum points of the e ective potential. The same model exhibits a family of traveling dark
solitons for every wave speed and we incorporate properties of these dark solitons for small wave speeds
in the analysis of orbital stability of the black soliton.
Keywords:
nonlinear Schrodinger equation; intensity-dependent dispersion; dark solitons; energetic stability; spectral stability;