Caption: Figure 15: Emergence of soliton trains according to KdV from initial

cosine wave. A = 0.3, T = 50.

[alpha] = [pi]/2, [beta] = 0, and the

cosine wave are taken to study the influence of the radius of the string on the energy density.

The 4th-order exciting force F for a phase angle of -34 degrees is expressed in Equation (5), so that the exciting forces for the phase angles of -34 degrees, -21 degrees and 0 degree are as shown in Figure 19, by using three

cosine waves.

6) The misalignments of the rail can be described by two types of curves: a complete or a half

cosine wave having the total length [lambda] and the amplitude [delta] (fig.

[omega](i, [t.sub.p]) [absolute value of ([r.sub.i])] is the frequency of the

cosine wave where [omega](i, [t.sub.p]) is a nonzero factor, and [phi](i) is the phase factor.

This means that two multipliers are used, one driven by the center frequency sine wave and the other by the

cosine wave.

The taper of the ridge may be in a shape approximating a

cosine wave or, if a very short transition is required, in the shape of steps.