We study stability of non-compact gradient Kähler-Ricci flow solitons with positive holomorphic bisectional curvature. Our main result is that any compactly supported perturbation and appropriately decaying perturbations of the Kähler potential of the soliton will converge to the original soliton under Kähler-Ricci flow as time tends to infinity. To obtain this result, we construct appropriate ...

This paper suggests a method to create dark soliton-like waves in a trapped atomic Bose-Einstein condensate (BEC). With the phase imprinting method, a soliton-like disturbance is produced along the x-axis. The method is used in two cases (with and without rotation of a trapping potential). The disturbance in a two-dimensional (2D) system is unstable. The soliton-like perturbation is found to de...

We study the dynamics of dark solitons in spatially inhomogeneous media with applications to cigar-shaped Bose–Einstein condensates trapped in a harmonic magnetic potential and a periodic potential representing an optical lattice. We distinguish and systematically investigate the cases with the optical lattice period being smaller, larger, or comparable to the width of the dark soliton. Analyti...

We study the time-domain quantum-noise properties of solitons in optical fibers. Perturbation theory, including quantum description of the continuum, is used to derive a complete analytical expression for the second-order correlator of the amplitude quadrature in time domain. This correlator is subsequently used to calculate the photon-number noise reduction below the standard quantum limit by ...

We analyze optical soliton propagation in the presence of weak absorption lines with much narrower linewidths as compared to the soliton spectrum width using the novel perturbation analysis technique based on an integral representation in the spectral domain. The stable soliton acquires spectral modulation that follows the associated index of refraction of the absorber. The model can be applied...

We study noise-induced perturbations of dispersion-managed solitons. We do so by first developing soliton perturbation theory for the dispersion-managed nonlinear Schrödinger DMNLS equation, which governs the long-term behavior of optical fiber transmission systems and certain kinds of femtosecond lasers. We show that the eigenmodes and generalized eigenmodes of the linearized DMNLS equation ar...

Collision of two solitons of the Manakov system is studied analytically. Existence of a complete polarization mode switching regime is proved and the parameters of solitons prepared for polarization switching are found. The idea of an analytical approach to the description of polarized (i.e., vector) solitons in nonlinear optical fibers is based on the fact [1] that for some values of the param...