Wavelet Analysis of Optical Solitons and its Energy Aspects

Abstract

In this study, wavelet theory is applied to analyze the solitons arising as the solution of non-linear Schrodinger equation (NLSE) which represents the behaviour of optical soliton in an optical fiber. In this study,wavelet transform (WT) in $L^{2}$ frame which makes use of soliton solution as its AW is proposed. Wavelet theory is applied to analyze the optical solitons arising as the solution of NLSE which represents the behaviour of optical soliton in an optical fiber. It is shown that the application of new Analyzing wavelet (AW) is very useful for the WT analysis of soliton interaction. Formulations of solitons as wavelets, reconstruction formula for soliton are obtained. Energy distribution in both in Continuous and discretized WT domain is discussed. Moreover, its relationship with Ambiguity functions in different forms and Space-Time-Variation (STV) wavelet operator and system's energy distribution are studied.