Boundary Value Problems For Integrable Equations Compatible With The Symmetry Algebra

Boundary value problems for integrable nonlinear partial differential equations are considered from the symmetry point of view. Families of boundary conditions compatible with the Harry-Dym, KdV and MKdV equations and the Volterra chain are discussed. We also discuss the uniqueness of some of these boundary conditions.Comment: 25 pages , Latex , no figure

On magnetic leaf-wise intersections

In this article we introduce the notion of a magnetic leaf-wise intersection point which is a generalization of the leaf-wise intersection point with magnetic effects. We also prove the existence of magnetic leaf-wise intersection points under certain topological assumptions.Comment: 43 page

Characterization of coupling of pump fluctuations to laser in mode-locked Yb-doped and Er-doped fiber oscillators

Transfer of fluctuations of pump power to laser power is characterized for mode-locked fiber oscillators. Contribution of pump noise to laser noise is estimated. Limits to pump modulation bandwidth for carrier-envelopephase stabilization are briefly discussed. © 2010 Optical Society of America

On the choice of basis functions to model surface electric current densities in computational electromagnetics

Basis functions that are used to model surface electric current densities in the electric field integral equations of computational electromagnetics are analyzed with respect to how well they model the charge distribution, in addition to the current. This analysis is carried out with the help of the topological properties of open and closed surfaces meshed into networks of triangles and quadrangles. The need for current basis functions to properly model the charge distribution is demonstrated by several examples. In some of these examples, the basis functions seem to be perfectly legitimate when only the current distribution is considered, but they fail to deliver a correct solution of the electromagnetic problem, since they are not capable of properly modeling the charge distribution on some surfaces. Although the idea of proper modeling of the charge distribution by the current basis functions is easy to accept and can even be claimed well known, the contrary uses encountered in the literature have been the motivation behind the investigation reported in this paper

Integrable boundary conditions for the Toda lattice

The problem of construction of the boundary conditions for the Toda lattice compatible with its higher symmetries is considered. It is demonstrated that this problem is reduced to finding of the differential constraints consistent with the ZS-AKNS hierarchy. A method of their construction is offered based on the B\"acklund transformations. It is shown that the generalized Toda lattices corresponding to the non-exceptional Lie algebras of finite growth can be obtained by imposing one of the four simplest integrable boundary conditions on the both ends of the lattice. This fact allows, in particular, to solve the problem of reduction of the series $A$ Toda lattices into the series $D$ ones. Deformations of the found boundary conditions are presented which leads to the Painlev\'e type equations. Key words: Toda lattice, boundary conditions, integrability, B\"acklund transformation, Lie algebras, Painlev\'e equation

Influence of pump noise on mode-locked fiber oscillators

Pump modulation transfer function (MTF), and its dependence on pump power are investigated for all normal dispersion, dispersion managed and soliton-like mode-locked oscillator both in experiment and simulation. We find that cavity losses and pulse instabilities such as multiple pulsing influence noise transfer, strongly. © OSA 2015

Influence of pump noise and modulation on in-fiber amplification of broadband pulses

We investigate experimentally and theoretically the coupling of pump laser modulation and noise fluctuations to the output power of a fiber amplifier for broadband pulse trains using the modulation transfer function approach. © 2010 Optical Society of America

Prediction of pulse-to-pulse intensity fluctuation characteristics of high power ultrafast fiber amplifiers

We report on the experimental characterization and theoretical prediction of pulse-to-pulse intensity fluctuations, namely, intensity noise, for ultrafast fiber amplifiers. We present a theoretical model with which the intensity noise of a Yb-doped fiber amplifier can be predicted with high accuracy, taking into account seed and pump noise, as well as generation of amplified spontaneous emission. Transfer of pump and seed signal modulations to the amplified output during fiber amplification are investigated thoroughly. Practically, our model enables design and optimization of fiber amplifiers with regards to their intensity noise performance. As a route to reducing noise imparted by pump diodes in a double-clad amplifier, we show the use of multiple, low-power diodes is more beneficial compared to a single, high-power diode due to the largely uncorrelated nature of their individual noise contributions. © 2014 AIP Publishing LLC