Monday, October 10, 1988 1:00 p.m.
As is well known, the nonlinear distortion of finite amplitude sound results from the fact that propagation speed depends on particle velocity and the nonlinearity parameter of the medium. In the case of a thin fiber of fused silica, the waveform of a finite amplitude sound is affected by velocity dispersion as well as nonlinear distortion. A soliton is formed when the waveform changes due to nonlinear distortion are balanced by those due to velocity dispersion. In this paper the soliton formation process is described by simulation using computer modeling.
Results obtained are as follows:
1) Solitary waves of hyperbolic form obeying the K-dV equation are found by computer simulation, not by solving the K-dV equation directly.
2) A waveform that is initially hyperbolic is changed in peak value and pulse width by the propagation until the condition of soliton formation is satisfied.
3) An initially sinusoidal wave is also changed by the propagation until the pulse form and its spectrum agree with those of the hyperbolic soliton.