## The scattering of solitons in classes of (1+1) …

**Consider the problem of initial partial collisions**. As it was discussed earlier for the case of classical solitons, initial partial collisions can be a serious problem by introducing large timing jitter at the output of transmission. On the other hand, for the classical case, one could avoid the half-collisions by staggering the pulse positions of the WDM channels at the transmission input. The situation is very different for the DM case. In the DM case,the collision length is usually longer than the distance between subsequent collisionsThus, a pulse can collide simultaneously with several pulses of another channel. The maximum number of such simultaneous collisions isNote that Nsc

This thesis presents research into the properties and features of the complex sine- Gordon theory. The CSG theory is a dimensional integrable held theory that admits soliton solutions which carry a Noether charge due to the U(I) invariance of the theory. Integrable CSG defects and boundaries are constructed and interactions between solitons, defects and boundaries are analysed at the classical and quantum level. The introduction of defects into the theory is facilitated by a new Backlund transformation involving two parameters. Defect conditions, constructed so they maintain the integrability of the theory and found to be exactly the BT, are used to sew two CSG theories together. How solitons interact with the defect is investigated, in particular whether as in the SG theory solitons can be absorbed and emitted by the defect. The classical time-delay and phase-shift are calculated for soliton-defect and particle-defect scattering. Using the CSG defect to dress the Dirichlet boundary a new CSG boundary theory is produced. Its integrability is checked by the explicit construction of conserved charges. The various interactions between solitons and the boundary are analysed, compared and contrasted with the defect theory. Finally aspects of the quantum CSG boundary theory are examined, culminating in a conjecture for the quantum reflection matrix for a Q = -1-1 soliton reflecting from an unexcited boundary. Reflection and boundary bootstrap procedures are used to generate the general reflection matrix for any charged soliton reflecting from any excited boundary

## On solitons for the Ricci flow - ResearchGate

2014, *New modelling applications for Helmholtz soliton theory: from single interfaces to waveguide arrays* , PhD thesis, University of Salford.

## Optical_Solitons | Soliton | Diffraction

**It is interesting to compare these results with the results** for the case of classical solitons (Eqs. 17-22). The time shifts per complete collisions (Eqs. 18 and 31) are about the same, the time shifts from all initial partial collisions (Eqs. 20 and 33) are also close to each other. The total maximum time shifts from all collisions are also close to each other for the case of long distance transmission. That means that, similar to the classical case, one has to control the collision-induced timing jitter when it becomes too large. As it was discussed earlier, the sliding frequency-guiding filters are very effective in suppressing the timing jitter. Because the collision length in DM systems is much longer than in classical systems, and, at the same time, it is almost independent of the channel wavelength separation, the requirement that the collision length is much greater than the filter spacing, Lcoll >> Lf, is easy to meet. As a result, the guiding filters suppress the timing jitter in DM systems even more effective than in classical soliton systems. The fact that the frequency excursions during collisions are much smaller in DM case, also makes the filters to work more effectively.

## Abstract of Ph.D Thesis (Or Peleg)-Physics

**As we have discussed previously**, many important features of DM solitons come from the fact that the soliton spectral bandwidth oscillates with the distance. That is why guiding filters alter the dispersion management itself and give an additional degree of freedom in the system design.60 Note also that the position of the filters in the dispersion map can change the soliton stability in some cases.61 It should also be noted that because of the weak dependence of the DM soliton spectral bandwidth on the soliton pulse energy, the energy fluctuations damping length provided by the guided filters is considerably longer than the frequency damping length.62 This is the price one has to pay for many advantages of DM soli-tons. From the practical point of view, the most important advantage is the flexibility in system design and freedom in choosing the transmission fibers. For example, one can upgrade existing systems by providing an appropriate dispersion compensation with dispersion compensation fibers or with lumped dispersion compensators (fiber Bragg gratings, for example). The biggest advantage of DM systems is the possibility to design dispersion maps with essentially zero dispersion slope of the path-average dispersion, dDav/dX, by combining commercially available fibers with different signs of dispersion and dispersion slopes. (Note that it was a nonzero dispersion slope that limited the maximum number of channels in classical soliton long distance WDM transmission.) This was demonstrated in the experiment where almost flat average dispersion, Dav = 0.3 ps nm-1 km-1 was achieved by combining standard, dispersion-compensating, and True-Wave (Lucent nonzero dispersion-shifted) fibers.63 By using sliding frequency-guiding filters and this dispersion map, "error-free" DM soliton transmission of twenty-seven 10-Gbit/s WDM channels was achieved over more than 9000 km without using forward error correction. It was shown that once the error-free transmission with about 10 channels is achieved, adding additional channels practically does not change performance of the system. (This is because, for each channel, only the nearest neighboring channels degrade its performance.) The maximum number of WDM channels in this experiment was limited only by the power and bandwidth of optical amplifiers used in the experiment. One can expect that the number of channels can be increased by a few times if more powerful and broader-bandwidth amplifiers are used.