Abstract—Many physical phenomena are described by nonlinear partial differential equations. These equations have soliton solutions which exhibit wavelet features called wavelet like solitons. Such wavelet like solitons have expansions in Gaussian family wavelets. In this work, using the fact that the wavelet like soliton has Gaussian representation, multiresolution analysis which is based on wavelets is carried out to obtain better approximation with the application of wavelet- Galerkin and wavelet-Petrokov-Galerkin methods for soliton solution of Korteweg-de Vries equation which appears in the study of waves in shallow water in the fluid dynamics. In the end, experimental data processing employing Gaussian representation of soliton solution is discussed.

Index Terms—Wavelet like solitons, gaussian representation, wavelet decomposition, data processing.

B. Bhosale is with the S.H.Kelkar College, affiliated to University of Mumbai, India (e-mail: bn.bhosale@rediffmail.com).
A. Biwas is with the Delaware State University in Dover, USA.

Cite:B. Bhosale and A. Biwas, "Multi-Resolution Analysis of Wavelet Like Soliton Solutions of KdV Equations," International Journal of Applied Physics and Mathematics vol. 3, no. 4, pp. 270-274, 2013.