We demonstrate that such distinct equations as the KdV, mKdV, NLS as well as the Calogero–Degasperis, Toda and Volterra equations can generated from each other via the discrete symmetries chains. Interestingly, the key ingredient in this process is none other but the famous KP equations.
A new way of construction of exact solutions describing the shape and the dynamics of vortex filaments is described. The new method is based on application of a binary Darboux transformation to the solutions of the nonlinear Schrödinger equation. A new type of solutions is constructed: the impacton. The explicit form of the curvature and torsion of corresponding vortex filament are calculated.
The paper discusses the stages of simulation of large infrastructure projects on the basis of the aggregate method. It is proved that the different stages of the life-cycle units is best modeled using different approaches. In addition, in order to implement energy-saving technologies is advisable to use a system of continuous time using a more complex mathematical structures (mostly– queuing systems).
A modified method of monitoring optical fibers in the fiber-optic communication lines is presented. Its implementation will allow to more accurately determine the location of the damaged area, to reduce the cost of service lines, to improve the reliability of fiber-optic cables in terms of external negative influences.