Sasa-Satsuma hierarchy of integrable evolution equations.

We present the infinite hierarchy of Sasa-Satsuma evolution equations. The corresponding Lax pairs are given, thus proving its integrability. The lowest order member of this hierarchy is the nonlinear Schrödinger equation, while the next one is the Sasa-Satsuma equation that includes third-order terms.

Asymptotically stable compensation of the soliton self-frequency shift.

We report on the stable cancellation of the soliton self-frequency shift (SSFS) in nonlinear optical fibers. A soliton, which scatters a group velocity matched pump wave in a so-called optical event horizon regime, may experience a blueshift in frequency, which counteracts the SSFS induced by Raman scattering. The SSFS can easily be compensated by a suitably prepared pump wave, but usually the compensation is unstable and is destroyed after a certain propagation length.

Influence of blood-brain barrier permeability on O-(2-F-fluoroethyl)-L-tyrosine uptake in rat gliomas.

Purpose: O-(2-F-fluoroethyl)-L-tyrosine (F-FET) is an established tracer for the diagnosis of brain tumors with PET. This study investigates the influence of blood-brain barrier (BBB) permeability on F-FET uptake in two rat glioma models and one human xenograft model.

Methods: F98 glioma, 9L gliosarcoma or human U87 glioblastoma cells were implanted into the striatum of 56 Fischer or RNU rats.

Infinite hierarchy of nonlinear Schrödinger equations and their solutions.

We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that "even- order" equations in the set affect phase and "stretching factors" in the solutions, while "odd-order" equations affect the velocities.

Spectral properties of limiting solitons in optical fibers.

It seems to be self-evident that stable optical pulses cannot be considerably shorter than a single oscillation of the carrier field. From the mathematical point of view the solitary solutions of pulse propagation equations should loose stability or demonstrate some kind of singular behavior. Typically, an unphysical cusp develops at the soliton top, preventing the soliton from being too short.