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The motivation of this work is to analyse the nonlinear models and their complex nature with generalized tools associated with material and history-based properties. With the help of well-known and widely used numerical scheme, we study the stimulating behaviours of the financial system in this work. The impact of parameters on price index, rate of interest, investment demand, influence changes and investment cost with respect to saving amount, and the elasticity of commercial markets demand are discussed. The consequences of generalizing the model within the arbitrary order are derived. The existence of the solution for the considered system is presented. This study helps beginner researchers to investigate complex real-world problems and predict the corresponding consequences. [ABSTRACT FROM AUTHOR]

In this paper, using the Extended Trial Equation (ETEM), we get new traveling wave solutions of the Generalized Benjamin, the Generalized Burger-Kdv Equations (GBE, GBKE). The obtained solutions not only constitute a novel analytical viewpoint in nonlinear complex phenomena, but they also form a new stand alone basis from which physical applications in this arena can be comprehended further, and moreover investigated. Furthermore, to concretely enrich this research production, we provide illustrative, Mathematica Release 7 based, 3D graphics of the gotten solutions, with well chosen, yet structure revealing parameters. [ABSTRACT FROM AUTHOR]

In this manuscript, we consider the Bernoulli sub-equation function method for obtaining new exponential prototype structures to the Cahn–Allen mathematical model. We obtained new results using this technique. We plotted two- and three-dimensional surfaces of the results using Wolfram Mathematica 9. At the end of this manuscript, we submitted a conclusion in a comprehensive manner. [ABSTRACT FROM AUTHOR]