Stationary pulse solutions of the cubic-quintic complex Ginzburg-Landau equation are related to heteroclinic orbits in a three-dimensional dynamical systems and they are usually obtained using numerical simulation. The harmonic balance method has severe limitation in computing homoclinic/heteroclinic orbits since the period of such orbits is infinite. In this paper, we present a perturbation-in...

Consider a one-mass system with two degrees of freedom, nonlin-early coupled, with parametric excitation in one direction. Assuming the internal resonance 1:2 and parametric resonance 1:2 we derive conditions for stability of the trivial solution by using both the harmonic balance method and the normal form method of averaging. If the trivial solution becomes unstable a stable periodic solution...

This paper detects the disturbing loads in distorted and/or unbalanced three phase three wire power system. It is based on the simultaneous measurement of four non-active power quantities, which are found on the IEEE Std.1459-2000 method. It allows, achieving better knowledge of the power system when both harmonic distortion and un-balance are present. The proposed method requires only the fund...

The influence of permanent dipole moments of quantized states on intersubband second harmonic generation based on quantum-interference induced transparency in semiconductor quantum wells is explored using the harmonic balance method. The permanent moments are found to be quite important: they affect the transparency condition, especially at larger pump intensities. Hence, both the conversion ef...

To predict nonlinear circuit behaviour, harmonic balance (HB) is a popular and useful frequency-domain technique. But given its mathematical nature, it can only converge to mathematical solutions being harmonically related to the input sources into the circuit. Nevertheless, the mathematical solutions to a nonlinear system do not necessarily need to be harmonically related to the input signals ...