Change of a period and tone-burst sinusoidal sounds to a stable soliton in a thin fiber of fused silica, under comparison with hyperbolic solitons

Abstract

Soliton formation processes for various waveforms given initially at an origin by using a valid computer algorithm will be discussed. Results obtained are as follows. The propagation behavior of a hyperbolic soliton governed by aKdV equation is described by three parameters which are pulse height, pulse width, and soliton velocity. A proportional relationship is found among these parameters. If a definite proportional constant is found in any propagation distance, it may be recognized that it is stable. In a dissipative medium, a different proportional constant from the one in a nondissipative medium is found. A negative sinusoidal pulse is changed to a hyperbolic one with propagation, while a positive pulse does not show any soliton. A period of sinusoidal waveform gives a soliton changing from a negative pressure part being in the waveform. The tone burst of a sinusoid with some wavelets also makes successively some solitons from the negative pressure part in the leading period to the one in the following period.