Abstract The cubic complex Ginzburg-Landau equation is one of the most-studied nonlinear
equations in the physics community. It describes a vast variety of phenomena from nonlinear …

This review paper presents an overview of the theoretical and experimental progress on the
study of matter-wave dark solitons in atomic Bose–Einstein condensates. Upon introducing …

Page 1 The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse Catherine
Sulem Pierre-Louis Sulem Springer Page 2 Applied Mathematical Sciences Volume 139 Editors …

Optical vortex-soliton filaments are observed in a bulk self-defocusing Kerr nonlinear
refractive medium. The dark cylindrical core, located at the axis of a 2π helical phase ramp …

Nonlinear systems with periodic variations of nonlinearity and/or dispersion occur in a
variety of physical problems and engineering applications. The mathematical concept of …

We study the dynamics of a supersonically expanding, ring-shaped Bose-Einstein
condensate both experimentally and theoretically. The expansion redshifts long-wavelength …

We analyze a transverse instability of plane (quasi-one-dimensional) dark solitons in the
framework of the two-dimensional nonlinear Schrödinger (NLS) equation for beam …

Composites consisting of metal nanoparticles (NPs) embedded in dielectric media may
present large nonlinear optical response due to electronic transitions in the NPs. When the …

There is considerable fundamental and applicative interest in obtaining nondiffractive and
nondispersive spatiotemporal localized wave packets propagating in optical cubic nonlinear …

We present a comprehensive analytical theory of localized nonlinear excitations—dark
solitons—supported by an incoherently pumped, spatially homogeneous exciton-polariton …