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We investigate the electromagnetic wave behavior and its characterization using collective variables technique. Second-order dispersion, first- and second-order nonlinearities, which strongly act in a left-handed nonlinear transmission line with series varactor diodes, are taken into account. Four frequency ranges have been found. The first one gives the so-called energetic soliton due to a perfect combination of second-order dispersion and first-order nonlinearity. The second frequency range presents a dispersive soliton leading to the collapse of the electromagnetic wave at the third frequency range. But the fourth one shows physical conditions which are able to provoke the appearance of wave trains generation with some particular waves, the rogue waves. Moreover, we demonstrate that the number of rogue waves increases with frequency. The soliton, thereafter, gains a relative stability when second-order nonlinearity comes into play with some specific values in the fourth frequency range. Furthermore, the stability conditions of the electromagnetic wave at high frequencies have been also discussed. [ABSTRACT FROM AUTHOR]

Based on ceramics S-shaped left-handed materials with magnetic resonance and electric anti-resonance were prepared by screen printing. The microwave transmittance properties of these samples in a rectangular waveguide were experimentally investigated. It is found that the two frequency bands of negative effective permittivity and negative effective permeability overlap from 8.5 to 9.46 GHz, which is left-handed materials pass-band and the bandwidth is about 1 GHz. Magnetic resonance is due to magnetic coupling between magnetic field component of external fields and the samples, in which the effective permeability could be negative. And electrical anti-resonance originated from electric coupling may contribute to negative effective permittivity. This based on ceramics substrate S-shaped construct possess both remarkable electric and magnetic resonances, which provides a flexible element for constructing planar left-handed materials. [ABSTRACT FROM AUTHOR]