In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction dispersion relation. This phenomenon can manifest either as a frequency shift or wavenumber depending whether excitation prescribed initial condition boundary condition, respectively. Several models have been proposed to capture shifts observed when system subjected harmon...

We consider complementary dynamical systems related to stationary Korteweg-de Vries hierarchy of equations. A general approach for finding elliptic solutions is given. The solutions are expressed in terms of Novikov polynomials in general quasi-periodic case. For periodic case these polynomials coincide with Hermite and Lamé polynomials. As byproduct we derive 2 × 2 matrix Lax representation fo...

The polybenzene units BTX 48, X=A (armchair) and X=Z (zig-zag) dimerize forming “eclipsed” isomers, the oligomers of which form structures of five-fold symmetry, called multi-tori. Multi-tori can be designed by appropriate map operations. The genus of multi-tori was calculated from the number of tetrapodal units they consist. A description, in terms of Omega polynomial, of the two linearly peri...

The finite-difference time-domain (FDTD) method is used to obtain numerical solutions of infinite periodic structures without resorting to the complex frequency-domain analysis, which is required in traditional frequency-domain techniques. The field transformation method is successfully used to model periodic structures with oblique incident waves/scan angles. Maxwell’s equations are transforme...

In this paper, a cellular neural networks with impulsive effects is investigated. By using differential inequality techniques, some very verifiable criteria on the existence and exponential stability of anti-periodic solutions for the model are obtained. Our results are new and complementary to previously known results. An example is included to illustrate the feasibility and effectiveness of o...

This paper develops a new design method for predictive repetitive control systems to track periodic reference signals or reject disturbances with bandlimited frequency content. In the presence of input disturbances acting on the system, the new design estimates these disturbances using an observer. This approach is complementary to the predictive repetitive control system designs previously rep...