Analysis of soliton solutions to the nonlinear schrodinger and konopelchenko-dubrovsky equations

Abstract

Many phenomena in the real world are described by nonlinear evolution equations (NLEEs), which have recently gained popularity. In this dissertation, we have explored two NLEEs to develop the generic and compatible closed form stable wave solutions by applying the (w/g)-expansion methods and the Modified Version of the New Kudryashov (MVNK) method. In this research, the (2+1)-dimensional paraxial nonlinear Schrodinger equation is investigated by the (w/g)-expansion methods. Also, the (2+1)- Konopelchenko–Dubrovsky (KD) equation is investigated via MVNK method. With the help of MATLAB, Wolfram Mathematica and Maple software, the solutions describe many forms of solitons and vary their nature and positions displayed in 3-dimensional and 2-dimensional figures for the values of Kerr nonlinearity, nonlinear coefficient, wave number, wave speed etc. Even so, it is found that the features of the solutions are crucial in parameter selection when comparing our results to existing literature produced using various methodologies and evaluating the solutions by drawing figures for various values of the corresponding parameters. Additionally, we show how the values of the various kinds of parameters relate to the physical justification of the determined solution. We have shown that the main reason why wave profiles behave differently when their associated free parameters change. The impacts of wave velocity and other free parameters on the wave profile are also examined. However, by sketching images of the solutions for different values of the associated parameters and examining the results of these approaches, it is evident that the solutions characteristics are greatly influenced by the parametric values. Although the facing few limitations, the techniques used are trustworthy, clear-cut, useful, and simple to apply.