Wavelet analysis of soliton interaction and its relation to probability distributions

Abstract

Non-linear processes, waves and oscillations occupy a special place in modern physics, radio physics and the wavelet analysis is a promising tool for describing non-linear wave processes. The mathematical methods based on it can be applied to the detection of new features of such non-linear processes. Many non-linear physical phenomena modelled by non-linear partial differential equations have soliton solutions and these solutions have wavelet features. Moreover, there exists a strong connectivity between wavelets, solitons and probability distributions. With this motivation, in this study, the wavelet analysis of solitons arising especially as the solution of the sine-Gordon equation is carried out using continuous wavelet transform and the connectivity between wavelets, solitons and probability distributions is discussed.