Wavelet analysis of soliton interaction

The wavelet transform (WT) is one type of representative time-frequency analysis. The characteristic of the WT is determined by the analyzing wavelet (AW). In this study, a WT which makes use of a hyperbolic function as its AW is proposed. The function describes the solution of the nonlinear Schrodinger (NLS) equation which represents the behavior of optical solitons in an optical fiber. The interaction between two simulated solitons is analyzed applying the new AW. Then, results obtained from the WT with the hyperbolic function as AW are compared with those from the WT with Gabor function. It is proved that the application of the new AW is very useful for the WT analysis of soliton interactions. Furthermore, to investigate the effect of noise components in a solution, analyses are made for the solutions of the NLS equation with spatial periodic perturbation of several levels. From this study, it is proved that the opto-soliton is quite appropriate for application to the information transmission system of optical fiber