Search

In this paper, partial differential equations with Dirichlet initial-boundary conditions is solved using an efficient numerical algorithms. A modified form of Adomian Decomposition Method (ADM) is implemented to construct the solution. Illustrative numerical examples are used to validate the proposed method. The results obtained indicate that this approach is indeed practical and efficient. [ABSTRACT FROM AUTHOR]

In this paper, the Adomian decomposition method and some modification of Adomian method are used for solving integro-differential equations arising in oscillating magnetic fields. Some numerical experiments are reported to illustrate the method. The results of applying this procedure to the integro-differential equation show the high accuracy, simplicity, and efficiency of this method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The complex modified KdV equation is studied in presence of perturbation terms with full nonlinearity. The soliton perturbation theory is applied to obtain the adiabatic dynamics of the soliton amplitude and frequency. The slow change in the soliton velocity is also obtained in presence of these perturbation terms. [ABSTRACT FROM AUTHOR]

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 Lr 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. [ABSTRACT FROM AUTHOR]

In this paper, the He's principles will be used to carry out the integration of the Rosenau-Kawahara equation. The variational iteration method as well as Homotopy perturbation method will be used to carry out the integration of this equation. Finally, the analytical method that is known as He's semi-inverse variational principle will also be used to obtain a closed form analytical 1-soliton solution to this equation. The numerical simulations are given to support the results. [ABSTRACT FROM AUTHOR]

This paper obtains the 1-soliton solution to the generalized Klein-Gordon equation, in presence of perturbation terms, by He's semi-inverse variational principle. There are two forms of nonlinearity that will be considered in this paper. [ABSTRACT FROM AUTHOR]

This paper obtains an exact l-soliton solution of the nonlinear Schrödinger's equation in 1+2 dimensions with parabolic law nonlinearity. The solitary wave ansatz is used to obtain this solution. In addition, a few of the conserved quantities are also computed using this exact solution. [ABSTRACT FROM AUTHOR]