R.M. Ross, P.G. Kevrekidis, and D.E. Pelinovsky
Localization in optical systems with an intensity-dependent dispersion
QUARTERLY OF APPLIED MATHEMATICS 79 (2021) 641-665
Abstract:
We address the nonlinear Schrodinger equation with intensity-dependent dispersion
which was recently proposed in the context of nonlinear optical systems. Contrary
to the previous findings, we prove that no solitary wave solutions exist if the sign of the
intensity-dependent dispersion coincides with the sign of the constant dispersion, whereas
a continuous family of such solutions exists in the case of the opposite signs. The family
includes two particular solutions, namely cusped and bell-shaped solitons, where the former
represents the lowest energy state in the family and the latter is a limit of solitary waves
in a regularized system. We further analyze the delicate analytical properties of these solitary
waves such as the asymptotic behavior near singularities, the spectral stability, and
the convergence of the fixed-point iterations near such solutions. The analytical theory is
corroborated by means of numerical approximations.
Keywords:
nonlinear Schrodinger equation, intensity-dependent dispersion, solitary waves,
behavior near singularities, fixed-point iterations